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Chapter 1Resource Masters
Geometry
Reading to Learn MathematicsVocabulary Builder
NAME ______________________________________________ DATE ____________ PERIOD _____
11
© Glencoe/McGraw-Hill vii Glencoe Geometry
Voca
bula
ry B
uild
erThis is an alphabetical list of the key vocabulary terms you will learn in Chapter 1.As you study the chapter, complete each term’s definition or description.Remember to add the page number where you found the term. Add these pages toyour Geometry Study Notebook to review vocabulary at the end of the chapter.
Vocabulary Term Found on Page Definition/Description/Example
acute angle
adjacent angles
uh·JAY·suhnt
angle
angle bisector
collinear
koh·LIN·ee·uhr
complementary angles
congruent
kuhn·GROO·uhnt
coplanar
koh·PLAY·nuhr
line segment
linear pair
(continued on the next page)
! " # " $
! " # " $
! " # " $
! " # " $
© Glencoe/McGraw-Hill viii Glencoe Geometry
Vocabulary Term Found on Page Definition/Description/Example
midpoint
obtuse angle
perimeter
perpendicular lines
polygon
PAHL·ee·gahn
ray
right angle
segment bisector
supplementary angles
vertical angles
! " # " $
Reading to Learn MathematicsVocabulary Builder (continued)
NAME ______________________________________________ DATE ____________ PERIOD _____
11
Study Guide and InterventionPoints, Lines, and Planes
NAME ______________________________________________ DATE ____________ PERIOD _____
1-11-1
© Glencoe/McGraw-Hill 1 Glencoe Geometry
Less
on
1-1
Name Points, Lines, and Planes In geometry, a point is a location, a line containspoints, and a plane is a flat surface that contains points and lines. If points are on the sameline, they are collinear. If points on are the same plane, they are coplanar.
Use the figure to name each of the following.
a. a line containing point A
The line can be named as !. Also, any two of the three points on the line can be used to name it.
AB!"#, AC!"#, or BC!"#
b. a plane containing point D
The plane can be named as plane N or can be named using three noncollinear points in the plane, such as plane ABD, plane ACD, and so on.
Refer to the figure.
1. Name a line that contains point A.
2. What is another name for line m ?
3. Name a point not on AC!"#.
4. Name the intersection of AC!"# and DB!"#.
5. Name a point not on line ! or line m .
Draw and label a plane Q for each relationship.
6. AB!"# is in plane Q.
7. ST!"# intersects AB!"# at P.
8. Point X is collinear with points A and P.
9. Point Y is not collinear with points T and P.
10. Line ! contains points X and Y.
!Q
AB
S
P
TY
X
!
Pm
AB
EC
D
!
N
AB
C
DExampleExample
ExercisesExercises
© Glencoe/McGraw-Hill 2 Glencoe Geometry
Points, Lines, and Planes in Space Space is a boundless, three-dimensional set ofall points. It contains lines and planes.
a. How many planes appear in the figure?
There are three planes: plane N , plane O, and plane P.
b. Are points A, B, and D coplanar?
Yes. They are contained in plane O.
Refer to the figure.
1. Name a line that is not contained in plane N.
2. Name a plane that contains point B.
3. Name three collinear points.
Refer to the figure.
4. How many planes are shown in the figure?
5. Are points B, E, G, and H coplanar? Explain.
6. Name a point coplanar with D, C, and E.
Draw and label a figure for each relationship.
7. Planes M andN intersect in HJ!"#.
8. Line r is in plane N , line s is in plane M, and lines r and sintersect at point J.
9. Line t contains point H and line t does not lie in plane M orplane N.
N
Ms
t
r
HJ
A B
CD
EF
G HI
J
N
A
C
B
DE
NO
P
AB
CD
Study Guide and Intervention (continued)
Points, Lines, and Planes
NAME ______________________________________________ DATE ____________ PERIOD _____
1-11-1
ExampleExample
ExercisesExercises
Skills PracticePoints, Lines, and Planes
NAME ______________________________________________ DATE ____________ PERIOD _____
1-11-1
© Glencoe/McGraw-Hill 3 Glencoe Geometry
Less
on
1-1
Refer to the figure.
1. Name a line that contains point D.
2. Name a point contained in line n.
3. What is another name for line p?
4. Name the plane containing lines n and p.
Draw and label a figure for each relationship.
5. Point K lies on RT!"#. 6. Plane J contains line s.
7. YP!"# lies in plane B and contains 8. Lines q and f intersect at point Zpoint C, but does not contain point H. in plane U.
Refer to the figure.
9. How many planes are shown in the figure?
10. How many of the planes contain points F and E?
11. Name four points that are coplanar.
12. Are points A, B, and C coplanar? Explain.
WA
B
E
C
DF
U
q f
Z
HP
B
CY
J
sTRK
G
n
A BD
C
p
© Glencoe/McGraw-Hill 4 Glencoe Geometry
Refer to the figure.
1. Name a line that contains points T and P.
2. Name a line that intersects the plane containing points Q, N, and P.
3. Name the plane that contains TN!"# and QR!"#.
Draw and label a figure for each relationship.
4. AK!"# and CG!"# intersect at point M 5. A line contains L(!4, !4) and M(2, 3). Line in plane T. q is in the same coordinate plane but does
not intersect LM!"#. Line q contains point N.
Refer to the figure.
6. How many planes are shown in the figure?
7. Name three collinear points.
8. Are points N, R, S, and W coplanar? Explain.
VISUALIZATION Name the geometric term(s) modeled by each object.
9. 10. 11.
12. a car antenna 13. a library card
strings
tip of pinSTOP
A M N
PW SX R
QT
L
M
N
q
x
y
O
KT
M
C
GA
S
j
g
hT
M
N
Q
R
P
Practice Points, Lines, and Planes
NAME ______________________________________________ DATE ____________ PERIOD _____
1-11-1
Reading to Learn MathematicsPoints, Lines, and Planes
NAME ______________________________________________ DATE ____________ PERIOD _____
1-11-1
© Glencoe/McGraw-Hill 5 Glencoe Geometry
Less
on
1-1
Pre-Activity Why do chairs sometimes wobble?
Read the introduction to Lesson 1-1 at the top of page 6 in your textbook.
• Find three pencils of different lengths and hold them upright on yourdesk so that the three pencil points do not lie along a single line. Can youplace a flat sheet of paper or cardboard so that it touches all three pencilpoints?
• How many ways can you do this if you keep the pencil points in the sameposition?
• How will your answer change if there are four pencil points?
Reading the Lesson
1. Complete each sentence.
a. Points that lie on the same lie are called points.
b. Points that do not lie in the same plane are called points.
c. There is exactly one through any two points.
d. There is exactly one through any three noncollinear points.
2. Refer to the figure at the right. Indicate whether each statement is true or false.
a. Points A, B, and C are collinear.
b. The intersection of plane ABC and line m is point P.
c. Line ! and line m do not intersect.
d. Points A, P,and B can be used to name plane U.
e. Line ! lies in plane ACB.
3. Complete the figure at the right to show the following relationship: Lines !, m, and n are coplanar and lie in plane Q. Lines ! and m intersect at point P. Line nintersects line m at R, but does not intersect line !.
Helping You Remember
4. Recall or look in a dictionary to find the meaning of the prefix co-. What does this prefixmean? How can it help you remember the meaning of collinear?
Qn
m
!P
R
U
m
!PC
D
B
A
© Glencoe/McGraw-Hill 6 Glencoe Geometry
Points and Lines on a MatrixA matrix is a rectangular array of rows and columns. Points andlines on a matrix are not defined in the same way as in Euclideangeometry. A point on a matrix is a dot, which can be small orlarge. A line on a matrix is a path of dots that “line up.” Betweentwo points on a line there may or may not be other points. Threeexamples of lines are shown at the upper right. The broad line canbe thought of as a single line or as two narrow lines side by side.
Dot-matrix printers for computers used dots to form characters.The dots are often called pixels. The matrix at the right showshow a dot-matrix printer might print the letter P.
Draw points on each matrix to create the given figures.
1. Draw two intersecting lines that have 2. Draw two lines that cross but have four points in common. no common points.
3. Make the number 0 (zero) so that it 4. Make the capital letter O so that itextends to the top and bottom sides extends to each side of the matrix.of the matrix.
5. Using separate grid paper, make dot designs for several other letters. Which were theeasiest and which were the most difficult?
Enrichment
NAME ______________________________________________ DATE ____________ PERIOD _____
1-11-1
Study Guide and InterventionLinear Measure and Precision
NAME ______________________________________________ DATE ____________ PERIOD _____
1-21-2
© Glencoe/McGraw-Hill 7 Glencoe Geometry
Less
on
1-2
Measure Line Segments A part of a line between two endpoints is called a linesegment. The lengths of M!N! and R!S! are written as MN and RS. When you measure asegment, the precision of the measurement is half of the smallest unit on the ruler.
Find the length of M!N!.
The long marks are centimeters, and theshorter marks are millimeters. The length of M!N! is 3.4 centimeters. The measurement is accurate to within 0.5 millimeter, so M!N! isbetween 3.35 centimeters and 3.45centimeters long.
1cm 2 3 4
M NFind the length of R!S!.
The long marks are inches and the short marks are quarter inches. The length of R!S!is about 1"
34" inches. The measurement is
accurate to within one half of a quarter inch,or "
18" inch, so R!S! is between 1"
58" inches and
1"78" inches long.
1 2in.
R S
Example 1Example 1 Example 2Example 2
ExercisesExercises
Find the length of each line segment or object.
1. 2.
3. 4.
Find the precision for each measurement.
5. 10 in. 6. 32 mm 7. 44 cm
8. 2 ft 9. 3.5 mm 10. 2"12" yd
1cm 2 31 2in.
1in.
S T
1cm 2 3
A B
© Glencoe/McGraw-Hill 8 Glencoe Geometry
Calculate Measures On PQ!"#, to say that point M is between points P and Q means P, Q, and M are collinear and PM # MQ $ PQ.
On AC!"#, AB $ BC $ 3 cm. We can say that the segments arecongruent, or A!B! " B!C!. Slashes on the figure indicate whichsegments are congruent.
AB
C
QMP
Study Guide and Intervention (continued)
Linear Measure and Precision
NAME ______________________________________________ DATE ____________ PERIOD _____
1-21-2
Find EF.
Calculate EF by adding ED and DF.
ED # DF $ EF1.2 # 1.9 $ EF
3.1 $ EF
Therefore, E!F! is 3.1 centimeters long.
E1.2 cm 1.9 cm
FD
Find x and AC.
B is between A and C.
AB # BC $ ACx # 2x $ 2x # 5
3x $ 2x # 5x $ 5
AC $ 2x # 5 $ 2(5) # 5 $ 15
A x 2x CB
2x ! 5
Example 1Example 1 Example 2Example 2
ExercisesExercises
Find the measurement of each segment. Assume that the art is not drawn to scale.
1. R!T! 2. B!C!
3. X!Z! 4. W!X!
Find x and RS if S is between R and T.
5. RS $ 5x, ST $ 3x, and RT $ 48. 6. RS $ 2x, ST $ 5x # 4, and RT $ 32.
7. RS $ 6x, ST $12, and RT $ 72. 8. RS $ 4x, R!S! " S!T!, and RT $ 24.
Use the figures to determine whether each pair of segments is congruent.
9. A!B! and C!D! 10. X!Y! and Y!Z!X
Y Z
3x ! 5 5x " 1
9x2
A D
CB
11 cm
11 cm
5 cm5 cm
W Y
6 cm
XX ZY
3–4 in.31–2 in.
A C
6 in.
23–4 in. BR T2.0 cm 2.5 cm
S
Skills PracticeLinear Measure and Precision
NAME ______________________________________________ DATE ____________ PERIOD _____
1-21-2
© Glencoe/McGraw-Hill 9 Glencoe Geometry
Less
on
1-2
Find the length of each line segment or object.
1. 2.
Find the precision for each measurement.
3. 40 feet 4. 12 centimeters 5. 9"12" inches
Find the measurement of each segment.
6. N!Q! 7. A!C! 8. G!H!
Find the value of the variable and YZ if Y is between X and Z.
9. XY $ 5p, YZ $ p, and XY $ 25 10. XY $ 12, YZ $ 2g, and XZ $ 28
11. XY $ 4m, YZ $ 3m, and XZ $ 42 12. XY $ 2c # 1, YZ $ 6c, and XZ $ 81
Use the figures to determine whether each pair of segments is congruent.
13. B!E!, C!D! 14. M!P!, N!P! 15. W!X!, W!Z!
Y Z
WX
9 ft
5 ft 5 ft
N
P
M 10 yd
12 yd
12 ydE D
CB
5 m
2 m
3 m 3 m
F 9.7 mm HG
15 mmA4.9 cm 5.2 cm
CBQ1in. 11–
4 in.
NP
1 2in.
1cm 2 3 54
© Glencoe/McGraw-Hill 10 Glencoe Geometry
Find the length of each line segment or object.
1. 2.
Find the precision for each measurement.
3. 120 meters 4. 7"14" inches 5. 30.0 millimeters
Find the measurement of each segment.
6. P!S! 7. A!D! 8. W!X!
Find the value of the variable and KL if K is between J and L.
9. JK $ 6r, KL $ 3r, and JL $ 27 10. JK $ 2s, KL $ s # 2, and JL $ 5s ! 10
Use the figures to determine whether each pair of segments is congruent.
11. T!U!, S!W! 12. A!D!, B!C! 13. G!F!, F!E!
14. CARPENTRY Jorge used the figure at the right to make a pattern for a mosaic he plans to inlay on a tabletop. Name all of the congruent segments in the figure.
D
A
BF
E C
G H
EF
5x
6xD C
BA
12.9 in.
12.7 in.
W
T S
U
2 ft
2 ft
3 ft
3 ft
W 89.6 cm YX
100 cmA
11–4 in.23–
8 in.
DCP4.7 cm18.4 cm
SQ
1cm 2 3 541 2in.
E F
Practice Linear Measure and Precision
NAME ______________________________________________ DATE ____________ PERIOD _____
1-21-2
Reading to Learn MathematicsLinear Measure and Precision
NAME ______________________________________________ DATE ____________ PERIOD _____
1-21-2
© Glencoe/McGraw-Hill 11 Glencoe Geometry
Less
on
1-2
Pre-Activity Why are units of measure important?
Read the introduction to Lesson 1-2 at the top of page 13 in your textbook.
• The basic unit of length in the metric system is the meter. How manymeters are there in one kilometer?
• Do you think it would be easier to learn the relationships between thedifferent units of length in the customary system (used in the UnitedStates) or in the metric system? Explain your answer.
Reading the Lesson
1. Explain the difference between a line and a line segment and why one of these can bemeasured, while the other cannot.
2. What is the smallest length marked on a 12-inch ruler?What is the smallest length marked on a centimeter ruler?
3. Find the precision of each measurement.a. 15 cmb. 15.0 cm
4. Refer to the figure at the right. Which one of the following statements is true? Explain your answer.A!B! $ C!D! A!B! " C!D!
5. Suppose that S is a point on V!W! and S is not the same point as V or W. Tell whethereach of the following statements is always, sometimes, or never true.a. VS $ SWb. S is between V and W.c. VS # VW $ SW
Helping You Remember
6. A good way to remember terms used in mathematics is to relate them to everyday wordsyou know. Give three words that are used outside of mathematics that can help youremember that there are 100 centimeters in a meter.
A
B
4.5 cm 4.5 cmD
C
© Glencoe/McGraw-Hill 12 Glencoe Geometry
Points Equidistant from SegmentsThe distance from a point to a segment is zero if the point is on the segment. Otherwise, it is the length of the shortest segment from the point to the segment.
A figure is a locus if it is the set of all points that satisfy a set of conditions. The locus of all points that are "
14" inch
from the segment AB is shown by two dashed segments with semicircles at both ends.
1. Suppose A, B, C, and D are four different points, and consider the locus of all points x units from A!B! and x units from C!D!. Use any unit you findconvenient. The locus can take different forms. Sketch at least threepossibilities. List some of the things that seem to affect the form of the locus.
2. Conduct your own investigation of the locus of pointsequidistant from two segments. Describe your results on aseparate sheet of paper.
A BC D
P Q
R S
A
B
C
D
X
Y
A B
C DX Y
A B
Enrichment
NAME ______________________________________________ DATE ____________ PERIOD _____
1-21-2
Study Guide and InterventionDistance and Midpoints
NAME ______________________________________________ DATE ____________ PERIOD _____
1-31-3
© Glencoe/McGraw-Hill 13 Glencoe Geometry
Less
on
1-3
Distance Between Two Points
Distance on a Number Line Distance in the Coordinate Plane
AB $ |b ! a | or |a ! b |x
y
OC(1, –1)
A(–2, –1)
B(1, 3)
Pythagorean Theorem:
a2 # b2 $ c2
Distance Formula:
d $ #(x2 !!x1)2 #! (y2 !! y1)2!
A B
a b
Find AB.
AB $ |(!4) ! 2|$ |! 6|$ 6
"5 "4 "3 "2 "1 0 1 2 3
A B
Find the distance between A(!2, !1) and B(1, 3).
Example 1Example 1 Example 2Example 2
Pythagorean Theorem
(AB)2 $ (AC)2 # (BC)2
(AB)2 $ (3)2 # (4)2
(AB)2 $ 25
AB $ #25!$ 5
Distance Formula
d $ #(x2 !!x1)2 #! (y2 !! y1)2!AB $ #(1 ! (!!2))2!# (3 !! (!1))!2!AB $ #(3)2 #! (4)2!
$ #25!$ 5
Use the number line to find each measure.
1. BD 2. DG
3. AF 4. EF
5. BG 6. AG
7. BE 8. DE
Use the Pythagorean Theorem to find the distance between each pair of points.
9. A(0, 0), B(6, 8) 10. R(!2, 3), S(3, 15)
11. M(1, !2), N(9, 13) 12. E(!12, 2), F(!9, 6)
Use the Distance Formula to find the distance between each pair of points.
13. A(0, 0), B(15, 20) 14. O(!12, 0), P(!8, 3)
15. C(11, !12), D(6, 2) 16. E(!2, 10), F(!4, 3)
–10 –8 –6 –4 –2 0 2 4 6 8
A B C D E F G
ExercisesExercises
© Glencoe/McGraw-Hill 14 Glencoe Geometry
Midpoint of a Segment
Midpoint on a If the coordinates of the endpoints of a segment are a and b,
Number Line then the coordinate of the midpoint of the segment is "a #2
b".
Midpoint on a If a segment has endpoints with coordinates (x1, y1) and (x2, y2),
Coordinate Plane then the coordinates of the midpoint of the segment are $"x1 #
2x2", "
y1 #
2y2"%.
Find the coordinate of the midpoint of P!Q!.
The coordinates of P and Q are !3 and 1.
If M is the midpoint of P!Q!, then the coordinate of M is "!32# 1" $ "
!22" or !1.
M is the midpoint of P!Q! for P("2, 4) and Q(4, 1). Find thecoordinates of M.
M $ $"x1 #
2x2", "
y1 #
2y2"% $ $"!2
2# 4", "
4 #2
1"% or (1, 2.5)
Use the number line to find the coordinate of the midpoint of each segment.
1. C!E! 2. D!G!
3. A!F! 4. E!G!
5. A!B! 6. B!G!
7. B!D! 8. D!E!
Find the coordinates of the midpoint of a segment having the given endpoints.
9. A(0, 0), B(12, 8) 10. R(!12, 8), S(6, 12)
11. M(11, !2), N(!9, 13) 12. E(!2, 6), F(!9, 3)
13. S(10, !22), T(9, 10) 14. M(!11, 2), N(!19, 6)
–10 –8 –6 –4 –2 0 2 4 6 8
A B C D E F G
–3 –2 –1 0 1 2
P Q
Study Guide and Intervention (continued)
Distance and Midpoints
NAME ______________________________________________ DATE ____________ PERIOD _____
1-31-3
Example 1Example 1
Example 2Example 2
ExercisesExercises
Skills PracticeDistance and Midpoints
NAME ______________________________________________ DATE ____________ PERIOD _____
1-31-3
© Glencoe/McGraw-Hill 15 Glencoe Geometry
Less
on
1-3
Use the number line to find each measure.
1. LN 2. JL
3. KN 4. MN
Use the Pythagorean Theorem to find the distance between each pair of points.
5. 6.
7. K(2, 3), F(4, 4) 8. C(!3, !1), Q(!2, 3)
Use the Distance Formula to find the distance between each pair of points.
9. Y(2, 0), P(2, 6) 10. W(!2, 2), R(5, 2)
11. A(!7, !3), B(5, 2) 12. C(!3, 1), Q(2, 6)
Use the number line to find the coordinate of the midpoint of each segment.
13. D!E! 14. B!C!
15. B!D! 16. A!D!
Find the coordinates of the midpoint of a segment having the given endpoints.
17. T(3, 1), U(5, 3) 18. J(!4, 2), F(5, !2)
Find the coordinates of the missing endpoint given that P is the midpoint of N!Q!.
19. N(2, 0), P(5, 2) 20. N(5, 4), P(6, 3) 21. Q(3, 9), P(!1, 5)
–6 –4 –2 0 2 4 6 8 10 12
A B C D E
x
y
O
D
S
x
y
O
F
G
–6 –4 –2 0 2 4 6 8 10
J K L M N
© Glencoe/McGraw-Hill 16 Glencoe Geometry
Use the number line to find each measure.
1. VW 2. TV
3. ST 4. SV
Use the Pythagorean Theorem to find the distance between each pair of points.
5. 6.
Use the Distance Formula to find the distance between each pair of points.
7. L(!7, 0), Y(5, 9) 8. U(1, 3), B(4, 6)
Use the number line to find the coordinate of the midpoint of each segment.
9. R!T! 10. Q!R!
11. S!T! 12. P!R!
Find the coordinates of the midpoint of a segment having the given endpoints.
13. K(!9, 3), H(5, 7) 14. W(!12, !7), T(!8, !4)
Find the coordinates of the missing endpoint given that E is the midpoint of D!F!.
15. F(5, 8), E(4, 3) 16. F(2, 9), E(!1, 6) 17. D(!3, !8), E(1, !2)
18. PERIMETER The coordinates of the vertices of a quadrilateral are R(!1, 3), S(3, 3),T(5, !1), and U(!2, !1). Find the perimeter of the quadrilateral. Round to the nearest tenth.
–6 –4–10 –8 –2 0 2 4 6
P Q R S T
x
y
O
E
S
x
y
OM
Z
–6 –4–10 –8 –2 0 2 4 6 8
S T U V W
Practice Distance and Midpoints
NAME ______________________________________________ DATE ____________ PERIOD _____
1-31-3
Reading to Learn MathematicsDistance and Midpoints
NAME ______________________________________________ DATE ____________ PERIOD _____
1-31-3
© Glencoe/McGraw-Hill 17 Glencoe Geometry
Less
on
1-3
Pre-Activity How can you find the distance between two points without a ruler?
Read the introduction to Lesson 1-3 at the top of page 21 in your textbook.
• Look at the triangle in the introduction to this lesson. What is the specialname for A!B! in this triangle?
• Find AB in this figure. Write your answer both as a radical and as adecimal number rounded to the nearest tenth.
Reading the Lesson
1. Match each formula or expression in the first column with one of the names in thesecond column.
a. d $ #(x2 !!x1)2 #! ( y2 !! y1)2! i. Pythagorean Theorem
b. "a #
2b
" ii. Distance Formula in the Coordinate Plane
c. XY $ |a ! b| iii. Midpoint of a Segment in the Coordinate Plane
d. c2 $ a2 # b2 iv. Distance Formula on a Number Line
e. $"x1 #
2x2
", "y1 #
2y2
"% v. Midpoint of a Segment on a Number Line
2. Fill in the steps to calculate the distance between the points M(4, !3) and N(!2, 7).
Let (x1, y1) $ (4, !3). Then (x2, y2) $ ( , ).
d $ #!!!!( ! )2 # ( ! )2
MN $ #!!!!( ! )2 # ( ! )2
MN $ #!!( )2 # ( )2
MN $ #!!#
MN $ #!Find a decimal approximation for MN to the nearest hundredth.
Helping You Remember
3. A good way to remember a new formula in mathematics is to relate it to one you alreadyknow. If you forget the Distance Formula, how can you use the Pythagorean Theorem tofind the distance d between two points on a coordinate plane?
© Glencoe/McGraw-Hill 18 Glencoe Geometry
Lengths on a GridEvenly-spaced horizontal and vertical lines form a grid.
You can easily find segment lengths on a grid if the endpoints are grid-lineintersections. For horizontal or verticalsegments, simply count squares. For diagonal segments, use the PythagoreanTheorem (proven in Chapter 7). This theorem states that in any right triangle,if the length of the longest side (the sideopposite the right angle) is c and the twoshorter sides have lengths a and b, then c2 $ a2 # b2.
Find the measure of E!F! on the grid at the right. Locate a right triangle with E!F! as its longest side.
EF $ #22 # 5!2! $ #29! & 5.4 units
Find each measure to the nearest tenth of a unit.
1. I!J! 2. M!N! 3. R!S! 4. Q!S!
5. I!K! 6. J!K! 7. L!M! 8. L!N!
Use the grid above. Find the perimeter of each triangle to the nearest tenth of a unit.
9. ! ABC 10. !QRS 11. ! DEF 12. ! LMN
13. Of all the segments shown on the 14. On the grid, 1 unit $ 0.5 cm. How can the grid, which is longest? What is its answers above be used to find the measures length? in centimeters?
15. Use your answer from exercise 8 to 16. Use a centimeter ruler to find the perimeter calculate the length of segment LN of triangle IJK to the nearest tenth of a in centimeters. Check by measuring centimeter.with a centimeter ruler.
E
2
5 F
A
B
F
I
J
K N M
C
D
E
S
R
Q
L
Enrichment
NAME ______________________________________________ DATE ____________ PERIOD _____
1-31-3
ExampleExample
Study Guide and InterventionAngle Measure
NAME ______________________________________________ DATE ____________ PERIOD _____
1-41-4
© Glencoe/McGraw-Hill 19 Glencoe Geometry
Less
on
1-4
Measure Angles If two noncollinear rays have a common endpoint, they form an angle. The rays are the sides of the angle.The common endpoint is the vertex. The angle at the right can be named as "A, "BAC, "CAB, or "1.
A right angle is an angle whose measure is 90. An acute anglehas measure less than 90. An obtuse angle has measure greater than 90 but less than 180.
A C
B
1
a. Name all angles that have R as avertex.Three angles are "1, "2, and "3. Forother angles, use three letters to namethem: "SRQ, "PRT, and "SRT.
b. Name the sides of !1.
RS""#, RP""#
S R T
PQ
1 2 3
Measure each angle andclassify it as right, acute, or obtuse.
a. !ABDUsing a protractor, m"ABD $ 50.50 % 90, so "ABD is an acute angle.
b. !DBCUsing a protractor, m"DBC $ 115.180 & 115 & 90, so "DBC is an obtuseangle.
c. !EBCUsing a protractor, m"EBC $ 90."EBC is a right angle.
BA
D E
C
Example 1Example 1 Example 2Example 2
ExercisesExercises
Refer to the figure.
1. Name the vertex of "4.
2. Name the sides of "BDC.
3. Write another name for "DBC.
Measure each angle in the figure and classify it as right,acute, or obtuse.
4. "MPR
5. "RPN
6. "NPS
P
NM
R
S
C
BA
12
34
D
© Glencoe/McGraw-Hill 20 Glencoe Geometry
Congruent Angles Angles that have the same measure are congruent angles. A ray that divides an angle into two congruent angles is called an angle bisector. In the figure, PN""# is the angle bisector of "MPR. Point N lies in the interior of "MPR and "MPN " "NPR.
Refer to the figure above. If m!MPN # 2x ! 14 and m!NPR # x ! 34, find x and find m!MPR.Since PN""# bisects "MPR, "MPN " "NPR, or m"MPN $ m"NPR.
2x # 14 $ x # 34 m"NPR $ (2x # 14) # (x # 34)2x # 14 ! x $ x # 34 ! x $ 54 # 54
x # 14 $ 34 $ 108x # 14 ! 14 $ 34 ! 14
x $ 20
QS!!" bisects !PQT, and QP!!" and QR!!" are opposite rays.
1. If m"PQT $ 60 and m"PQS $ 4x # 14, find the value of x.
2. If m"PQS $ 3x # 13 and m"SQT $ 6x ! 2, find m"PQT.
BA!!" and BC!!" are opposite rays, BF!!" bisects !CBE, and BD!!" bisects !ABE.
3. If m"EBF $ 6x # 4 and m"CBF $ 7x ! 2, find m"EBC.
4. If m"1 $ 4x # 10 and m"2 $ 5x, find m"2.
5. If m"2 $ 6y # 2 and m"1 $ 8y ! 14, find m"ABE.
6. Is "DBF a right angle? Explain.
BA C
F
ED
12 3
4
QP R
TS
P R
NM
Study Guide and Intervention (continued)
Angle Measure
NAME ______________________________________________ DATE ____________ PERIOD _____
1-41-4
ExampleExample
ExercisesExercises
Skills PracticeAngle Measure
NAME ______________________________________________ DATE ____________ PERIOD _____
1-41-4
© Glencoe/McGraw-Hill 21 Glencoe Geometry
Less
on
1-4
For Exercises 1–12, use the figure at the right.
Name the vertex of each angle.
1. "4 2. "1
3. "2 4. "5
Name the sides of each angle.
5. "4 6. "5
7. "STV 8. "1
Write another name for each angle.
9. "3 10. "4
11. "WTS 12. "2
Measure each angle and classify it as right, acute,or obtuse.
13. "NMP 14. "OMN
15. "QMN 16. "QMO
ALGEBRA In the figure, BA!!" and BC!!" are opposite rays,BD!!" bisects !EBC, and BF!!" bisects !ABE.
17. If m"EBD $ 4x # 16 and m"DBC $ 6x # 4,find m"EBD.
18. If m"ABF $ 7x ! 8 and m"EBF $ 5x # 10,find m"EBF.
B CA
FE
D
M NL
Q O
P
U
T
VW
S5 3
21
4
© Glencoe/McGraw-Hill 22 Glencoe Geometry
For Exercises 1–10, use the figure at the right.
Name the vertex of each angle.
1. "5 2. "3
3. "8 4. "NMP
Name the sides of each angle.
5. "6 6. "2
7. "MOP 8. "OMN
Write another name for each angle.
9. "QPR 10. "1
Measure each angle and classify it as right, acute,or obtuse.
11. "UZW 12. "YZW
13. "TZW 14. "UZT
ALGEBRA In the figure, CB!!" and CD!!" are opposite rays,CE!!" bisects !DCF, and CG!!" bisects !FCB.
15. If m"DCE $ 4x # 15 and m"ECF $ 6x ! 5,find m"DCE.
16. If m"FCG $ 9x # 3 and m"GCB $ 13x ! 9,find m"GCB.
17. TRAFFIC SIGNS The diagram shows a sign used to warn drivers of a school zone or crossing. Measure and classify each numbered angle. 2
1
B
C
G
F
ED
Z YT
U
V W
X
N
O
P Q
R
M12
8
3
54
6
7
Practice Angle Measure
NAME ______________________________________________ DATE ____________ PERIOD _____
1-41-4
Reading to Learn MathematicsAngle Measure
NAME ______________________________________________ DATE ____________ PERIOD _____
1-41-4
© Glencoe/McGraw-Hill 23 Glencoe Geometry
Less
on
1-4
Pre-Activity How big is a degree?
Read the introduction to Lesson 1-4 at the top of page 29 in your textbook.• A semicircle is half a circle. How many degrees are there in a
semicircle?• How many degrees are there in a quarter circle?
Reading the Lesson1. Match each description in the first column with one of the terms in the second column.
Some terms in the second column may be used more than once or not at all.a. a figure made up of two noncollinear rays with a 1. vertex
common endpoint 2. angle bisectorb. angles whose degree measures are less than 90 3. opposite raysc. angles that have the same measure 4. angled. angles whose degree measures are between 90 and 180 5. obtuse anglese. a tool used to measure angles 6. congruent anglesf. the common endpoint of the rays that form an angle 7. right anglesg. a ray that divides an angle into two congruent angles 8. acute angles
9. compass10. protractor
2. Use the figure to name each of the following.a. a right angleb. an obtuse anglec. an acute angled. a point in the interior of "EBCe. a point in the exterior of "EBAf. the angle bisector of "EBCg. a point on "CBEh. the sides of "ABFi. a pair of opposite raysj. the common vertex of all angles shown in the figurek. a pair of congruent anglesl. the angle with the greatest measure
Helping You Remember3. A good way to remember related geometric ideas is to compare them and see how they
are alike and how they are different. Give some similarities and differences betweencongruent segments and congruent angles.
B G
28$28$
A
EF
CD
© Glencoe/McGraw-Hill 24 Glencoe Geometry
Angle RelationshipsAngles are measured in degrees ('). Each degree of an angle is divid-ed into 60 minutes ((), and each minute of an angle is divided into 60 seconds ()).
60( $ 1'
60) $ 1(
67"12"' $ 67'30(
70.4' $ 70°24(
90' $ 89°60(
Two angles are complementary if the sum of their measures is 90$.Find the complement of each of the following angles.
1. 35'15( 2. 27'16( 3. 15'54(
4. 29'18(22) 5. 34'29(45) 6. 87'2(3)
Two angles are supplementary if the sum of their measures is 180$.Find the supplement of each of the following angles.
7. 120'18( 8. 84'12( 9. 110'2(
10. 45'16(24) 11. 39'21(54) 12. 129'18(36)
13. 98'52(59) 14. 9'2(32) 15. 1'2(3)
Enrichment
NAME ______________________________________________ DATE ____________ PERIOD _____
1-41-4
Study Guide and InterventionAngle Relationships
NAME ______________________________________________ DATE ____________ PERIOD _____
1-51-5
© Glencoe/McGraw-Hill 25 Glencoe Geometry
Less
on
1-5
Pairs of Angles Adjacent angles are angles in the same plane that have a commonvertex and a common side, but no common interior points. Vertical angles are twononadjacent angles formed by two intersecting lines. A pair of adjacent angles whosenoncommon sides are opposite rays is called a linear pair.
Identify each pair of angles as adjacent angles, vertical angles,and/or as a linear pair.
ExampleExample
a.
"SRT and "TRU have a commonvertex and a common side, but nocommon interior points. They areadjacent angles.
c.
"6 and "5 are adjacent angles whosenoncommon sides are opposite rays.The angles form a linear pair.
D
CBA
5 6
RU
TS
b.
"1 and "3 are nonadjacent angles formedby two intersecting lines. They are verticalangles. "2 and "4 are also vertical angles.
d.
"A and "B are two angles whose measureshave a sum of 90. They are complementary."F and "G are two angles whose measureshave a sum of 180. They are supplementary.
AB
F G
30$
60$
60$120$
N
RP
SM1
43
2
ExercisesExercises
Identify each pair of angles as adjacent, vertical, and/or as a linear pair.
1. "1 and "2 2. "1 and "6
3. "1 and "5 4. "3 and "2
For Exercises 5–7, refer to the figure at the right.
5. Identify two obtuse vertical angles.
6. Identify two acute adjacent angles.
7. Identify an angle supplementary to "TNU.
8. Find the measures of two complementary angles if the difference in their measures is 18.
R S
NU
T
V
R
S
TU
V
P
Q5
432
1 6
© Glencoe/McGraw-Hill 26 Glencoe Geometry
Perpendicular Lines Lines, rays, and segments that form four right angles are perpendicular. The right angle symbol indicates that the lines are perpendicular. In the figure at the right, AC!"# is perpendicular to BD!"#,or AC!"# ! BD!"#.
Find x so that D!Z! ! P!Z!.If D!Z! ! P!Z!, then m"DZP $ 90.
m"DZQ # m"QZP $ m"DZP Sum of parts $ whole
(9x # 5) # (3x # 1) $ 90 Substitution
12x # 6 $ 90 Simplify.12x $ 84 Subtract 6 from each side.
x $ 7 Divide each side by 12.
1. Find x and y so that NR!"# ! MQ!"#.
2. Find m"MSN.
3. m"EBF $ 3x # 10, m"DBE $ x, and BD""# ! BF""#. Find x.
4. If m"EBF $ 7y ! 3 and m"FBC $ 3y # 3, find y so that EB""# ! BC""#.
5. Find x, m"PQS, and m"SQR.
6. Find y, m"RPT, and m"TPW.
P
S
V
R
W
T(4y " 5)$
(2y ! 5)$
Q R
P S3x $
(8x ! 2)$
B CA
DE
F
M
N
R
S Q
Px $5x $
(9y ! 18)$
Z
D
P
Q(9x ! 5)$
(3x ! 1)$
B
CD
A
Study Guide and Intervention (continued)
Angle Relationships
NAME ______________________________________________ DATE ____________ PERIOD _____
1-51-5
ExampleExample
ExercisesExercises
Skills PracticeAngle Relationships
NAME ______________________________________________ DATE ____________ PERIOD _____
1-51-5
© Glencoe/McGraw-Hill 27 Glencoe Geometry
Less
on
1-5
For Exercises 1–6, use the figure at the right and a protractor.
1. Name two acute vertical angles.
2. Name two obtuse vertical angles.
3. Name a linear pair.
4. Name two acute adjacent angles.
5. Name an angle complementary to "EKH.
6. Name an angle supplementary to "FKG.
7. Find the measures of an angle and its complement if one angle measures 18 degreesmore than the other.
8. The measure of the supplement of an angle is 36 less than the measure of the angle.Find the measures of the angles.
ALGEBRA For Exercises 9–10, use the figure at the right.
9. If m"RTS $ 8x # 18, find x so that TR""# ! TS""#.
10. If m"PTQ $ 3y ! 10 and m"QTR $ y, find y so that "PTR is a right angle.
Determine whether each statement can be assumed from the figure. Explain.
11. "WZU is a right angle.
12. "YZU and "UZV are supplementary.
13. "VZU is adjacent to "YZX.
ZX
W
V
YU
TP
QR
S
K
G
J
FE
H
© Glencoe/McGraw-Hill 28 Glencoe Geometry
For Exercises 1–4, use the figure at the right and a protractor.
1. Name two obtuse vertical angles.
2. Name a linear pair whose vertex is B.
3. Name an angle not adjacent to but complementary to "FGC.
4. Name an angle adjacent and supplementary to "DCB.
5. Two angles are complementary. The measure of one angle is 21 more than twice themeasure of the other angle. Find the measures of the angles.
6. If a supplement of an angle has a measure 78 less than the measure of the angle, whatare the measures of the angles?
ALGEBRA For Exercises 7–8, use the figure at the right.
7. If m"FGE $ 5x # 10, find x so that FC!"# ! AE!"#.
8. If m"BGC $ 16x ! 4 and m"CGD $ 2x # 13,find x so that "BGD is a right angle.
Determine whether each statement can be assumed from the figure. Explain.
9. "NQO and "OQP are complementary.
10. "SRQ and "QRP is a linear pair.
11. "MQN and "MQR are vertical angles.
12. STREET MAPS Darren sketched a map of the cross streets nearest to his home for his friend Miguel. Describe two different anglerelationships between the streets. Olive
Beac
on
Main
Q
O
P
RS
M
N
GF
AB
E
D
C
DAE
HG
B C
F
Practice Angle Relationships
NAME ______________________________________________ DATE ____________ PERIOD _____
1-51-5
Reading to Learn MathematicsAngle Relationships
NAME ______________________________________________ DATE ____________ PERIOD _____
1-51-5
© Glencoe/McGraw-Hill 29 Glencoe Geometry
Less
on
1-5
Pre-Activity What kinds of angles are formed when streets intersect?
Read the introduction to Lesson 1-5 at the top of page 37 in your textbook.• How many separate angles are formed if three lines intersect at a common
point? (Do not use an angle whose interior includes part of another angle.)• How many separate angles are formed if n lines intersect at a common
point? (Do not count an angle whose interior includes part of another angle.)
Reading the Lesson1. Name each of the following in the figure at the right.
a. two pairs of congruent anglesb. a pair of acute vertical anglesc. a pair of obtuse vertical anglesd. four pairs of adjacent anglese. two pairs of vertical anglesf. four linear pairsg. four pairs of supplementary angles
2. Tell whether each statement is always, sometimes, or never true.a. If two angles are adjacent angles, they form a linear pair.b. If two angles form a linear pair, they are complementary.c. If two angles are supplementary, they are congruent.d. If two angles are complementary, they are adjacent.e. When two perpendicular lines intersect, four congruent angles are formed.f. Vertical angles are supplementary.g. Vertical angles are complementary.h. The two angles in a linear pair are both acute.i. If two angles form a linear pair, one is acute and the other is obtuse.
3. Complete each sentence.a. If two angles are supplementary and x is the measure of one of the angles, then the
measure of the other angle is .b. If two angles are complementary and x is the measure of one of the angles, then the
measure of the other angle is .
Helping You Remember4. Look up the nonmathematical meaning of supplementary in your dictionary. How can
this definition help you to remember the meaning of supplementary angles?
65$ 2 34
1
© Glencoe/McGraw-Hill 30 Glencoe Geometry
Curve StitchingThe star design at the right was created by a method known as curve stitching. Although the design appears to contain curves, it is made up entirely of line segments.
To begin the star design, draw a 60° angle. Mark eight equally-spaced points on each ray, and number the points as shown below. Then connect pairs of points that have the same number.
To make a complete star, make the same design in six 60° angles that have a common central vertex.
1. Complete the section of the star design above by connecting pairs of points that have the same number.
2. Complete the following design.
3. Create your own design. You may use several angles, and the angles may overlap.
1 2 3 4 5 6 7 8 9
11
11
12
13
14
15
16
17
18
19
1
2
3
4
5
6
7
8
9
12 13 14 15 16 17 18 19
8
7
6
5
4
3
2
1
1 2 3 4 5 6 7 8
Enrichment
NAME ______________________________________________ DATE ____________ PERIOD _____
1-51-5
Study Guide and InterventionPolygons
NAME ______________________________________________ DATE ____________ PERIOD _____
1-61-6
© Glencoe/McGraw-Hill 31 Glencoe Geometry
Less
on
1-6
Polygons A polygon is a closed figure formed by a finite number of coplanar linesegments. The sides that have a common endpoint must be noncollinear and each sideintersects exactly two other sides at their endpoints. A polygon is named according to itsnumber of sides. A regular polygon has congruent sides and congruent angles. A polygoncan be concave or convex.
Name each polygon by its number of sides. Then classify it asconcave or convex and regular or irregular.
ExampleExample
a.
The polygon has 4 sides, so it is a quadrilateral.It is concave because part of D!E! or E!F! lies in theinterior of the figure. Because it is concave, itcannot have all its angles congruent and so it isirregular.
c.
The polygon has 5 sides, so it is a pentagon. It isconvex. All sides are congruent and all angles arecongruent, so it is a regular pentagon.
D F
G
E b.
The figure is not closed, so it isnot a polygon.
d.
The figure has 8 congruent sidesand 8 congruent angles. It isconvex and is a regular octagon.
H
J K
LI
ExercisesExercises
Name each polygon by its number of sides. Then classify it as concave or convexand regular or irregular.
1. 2. 3.
4. 5. 6.
© Glencoe/McGraw-Hill 32 Glencoe Geometry
Perimeter The perimeter of a polygon is the sum of the lengths of all the sides of thepolygon. There are special formulas for the perimeter of a square or a rectangle.
Write an expression or formula for the perimeter of each polygon.Find the perimeter.
Study Guide and Intervention (continued)
Polygons
NAME ______________________________________________ DATE ____________ PERIOD _____
1-61-6
ExampleExample
a.
P $ a # b # c$ 3 # 4 # 5$ 12 in.
b.
P $ 4s$ 4(5)$ 20 cm
c.
P $ 2! # 2w$ 2(3) # 2(2)$ 10 ft
3 ft
2 ft
!
!
w w
5 cm
5 cm 5 cm
5 cm
s
s
s s3 in.5 in.
4 in.
a
b
c
ExercisesExercises
Find the perimeter of each figure.
1. 2.
3. 4.
Find the length of each side of the polygon for the given perimeter.
5. P $ 96 6. P $ 48x
x
2x
x " 2
rectangle
2x
x
1 cm
24 yd
19 yd
12 yd 14 yd
27 yd
square
5.5 ft
3.5 cm
3 cm2.5 cm
Skills PracticePolygons
NAME ______________________________________________ DATE ____________ PERIOD _____
1-61-6
© Glencoe/McGraw-Hill 33 Glencoe Geometry
Less
on
1-6
Name each polygon by its number of sides and then classify it as convex orconcave and regular or irregular.
1. 2. 3.
4. 5. 6.
Find the perimeter of each figure.
7. 8. 9.
COORDINATE GEOMETRY Find the perimeter of each polygon.
10. triangle ABC with vertices A(3, 5), B(3, 1), and C(0, 1)
11. quadrilateral QRST with vertices Q(!3, 2), R(1, 2), S(1, !4), and T(!3, !4)
12. quadrilateral LMNO with vertices L(!1, 4), M(3, 4), N(2, 1), and O(!2, 1)
ALGEBRA Find the length of each side of the polygon for the given perimeter.
13. P $ 104 millimeters 14. P $ 84 kilometers 15. P $ 88 feet4w " 1
w
10 in.
10 in.2 in. 2 in.
2 in.2 in.2 in. 2 in.
5 m2 m 3 m
6 m4 m
40 yd
20 yd
18 yd 20 yd
© Glencoe/McGraw-Hill 34 Glencoe Geometry
Name each polygon by its number of sides and then classify it as convex orconcave and regular or irregular.
1. 2. 3.
Find the perimeter of each figure.
4. 5. 6.
COORDINATE GEOMETRY Find the perimeter of each polygon.
7. quadrilateral OPQR with vertices O(!3, 2), P(1, 5), Q(6, 4), and R(5, !2)
8. pentagon STUVW with vertices S(0, 0), T(3, !2), U(2, !5), V(!2, !5), and W(!3, !2)
ALGEBRA Find the length of each side of the polygon for the given perimeter.
9. P $ 26 inches 10. P $ 39 centimeters 11. P $ 89 feet
SEWING For Exercises 12–13, use the following information.Jasmine plans to sew fringe around the scarf shown in the diagram.
12. How many inches of fringe does she need to purchase?
13. If Jasmine doubles the width of the scarf, how many inches of fringe will she need?
16 in.
4 in. 4 in.
16 in.
2x ! 2
x ! 9
5x " 4
3x ! 52x " 3
6n " 8
n
14 cm
14 cm
4 cm
4 cm 6 cm6 cm
6 cm2 cm
32 mi
33 mi21 mi
7 mm
10 mm18 mm
18 mm
Practice Polygons
NAME ______________________________________________ DATE ____________ PERIOD _____
1-61-6
Reading to Learn MathematicsPolygons
NAME ______________________________________________ DATE ____________ PERIOD _____
1-61-6
© Glencoe/McGraw-Hill 35 Glencoe Geometry
Less
on
1-6
Pre-Activity How are polygons related to toys?
Read the introduction to Lesson 1-6 at the top of page 45 in your textbook.
Name four different shapes that can each be formed by four sticks connected toform a closed figure. Assume you have sticks with a good variety of lengths.
Reading the Lesson
1. Tell why each figure is not a polygon.a. b. c.
2. Name each polygon by its number of sides. Then classify it as convex or concave andregular or not regular.a. b. c.
3. What is another name for a regular quadrilateral?
4. Match each polygon in the first column with the formula in the second column that canbe used to find its perimeter. (s represents the length of each side of a regular polygon.)
a. regular dodecagon i. P $ 8s
b. square ii. P $ 6s
c. regular hexagon iii. P $ a # b # c
d. rectangle iv. P $ 12s
e. regular octagon v. P $ 2! # 2w
f. triangle vi. P $ 4s
Helping You Remember
5. One way to remember the meaning of a term is to explain it to another person.How would you explain to a friend what a regular polygon is?
© Glencoe/McGraw-Hill 36 Glencoe Geometry
Enrichment
NAME ______________________________________________ DATE ____________ PERIOD _____
1-61-6
Perimeter and Area of Irregular ShapesTwo formulas that are used frequently in mathematics are perimeter andarea of a rectangle.
Perimeter: P $ 2! # 2wArea: A $ !w, where ! is the length and w is the width
However, many figures are combinations of two or more rectangles creatingirregular shapes. To find the area of an irregular shape, it helps to separatethe shape into rectangles, calculate the formula for each rectangle, then findthe sum of the areas.
Find the area of thefigure at the right.Separate the figure into two rectangles.
A $ !wA1 $ 9 * 2 A2 $ 3 * 3
$ 18 $ 9
18 # 9 $ 27
The area of the irregular shape is 27 m2.
Find the area and perimeter of each irregular shape.
1. 2.
3.4.
For Exercises 5–8, find the perimeter of the figures in Exercises 1–4.
5. 6. 7. 8.
9. Describe the steps you used to find the perimeter in Exercise 1.
9 ft
2 ft
3 ft
7 ft
6 ft
4 ft
8 cm
4 cm
2 cm
2 cm
4 cm
4 cm
6 cm
4 cm
9 m
26 m
6 m13 m7 m
12 m
2 in.
4 in. 4 in.
1 in.
9 m
3 m
1
25 m
2 m
9 m
3 m
5 m
2 m
ExampleExample
Chapter 1 Test, Form 111
© Glencoe/McGraw-Hill 37 Glencoe Geometry
Ass
essm
ents
Write the letter for the correct answer in the blank at the right of each question.
1. Name the geometric shape modeled by a pinhole in a wall.A. line segment B. plane C. line D. point
For Questions 2–4, use the figure given at the right.
2. Which is another name for line !?A. AB!"# B. BD!"#
C. C D. P
3. Name the intersection of lines ! and m.A. A B. BC. C D. P
4. Name three points coplanar with point A.A. B, C, F B. E, F, GC. B, C, E D. B, D, G
5. Find the length of R!S!.A. 33 mm B. 34 mmC. 35 mm D. 36 mm
6. Find the precision for a measurement of 72 centimeters.A. 0.5 cm B. 0.1 cmC. 1 mm D. 0.5 mm
7. Find the length of B!C!.A. 12 cm B. 13 cmC. 25 cm D. 38 cm
8. Use the number line to find MN.A. !5 B. 1C. 5 D. 10
For Questions 9 and 10, use the figure given at the right.
9. Find the distance between points P and Q.A. 5 B. 7C. 9 D. 25
10. Find the coordinates of the midpoint of P!Q!.
A. "2, 3"12"# B. "0, 3"
12"# C. (0, 3) D. "3"
12", 0#
x
y
O
P
Q
!5 !4 !3 !2 !1 0 1 2 3
M N
A C
25 cm
13 cm B
1cm 2 3 4
R S
!
P
m
AB
C
DE
G
F
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
NAME DATE PERIOD
SCORE
NAME DATE PERIOD
© Glencoe/McGraw-Hill 38 Glencoe Geometry
Chapter 1 Test, Form 1 (continued)11
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
For Questions 11–13, use the figure at the right.
11. Which point is the vertex of all the angles in this figure?A. A B. BC. C D. E
12. What type of angle is !ABC?A. acute angle B. right angle C. obtuse angle D. straight angle
13. Which is true?A. m!EBF # 140 B. m!EBF # 90 C. m!EBF # 50 D. m!EBF # 40
14. For what value of x is !ATK $ !MJS if m!ATK # 5x $ 4 and m!MJS # 8x ! 11?A. 29 B. 15 C. 10 D. 5
For Questions 15–17, use the figure at the right.
15. Which pair of angles are vertical angles?A. !RST, !TSU B. !RSX, !TSUC. !TSU, !USV D. !RSX, !XSW
16. Which angle is supplementary to !USV ?A. !TSU B. !VSW C. !RSV D. !WSR
17. Find x and y.A. x # 10, y # 12 B. x # 20, y # 7 C. x # 10, y # 8 D. x # 50, y # 40
For Questions 18–20, use the figures below.
18. Which figure is not a polygon?A. Figure A B. Figure B C. Figure C D. Figure D
19. Find the perimeter of the convex pentagon.A. 46 cm B. 50 cm C. 61 cm D. 72 cm
20. Suppose the length and width of the rectangle are doubled. What is itsperimeter?A. 120 cm B. 92 cm C. 76 cm D. 46 cm
Bonus Each side of a square is 2x ! 6 yards long. If the perimeter of the square is 72 yards what is the value of x?
8 cm
8 cm
8 cm
4 cm
15 cm15 cm
18 cm
18 cm
25 cm
15 cm
8 cm8 cm15 cm
12 cm
15 cm12 cmFigure A Figure DFigure B Figure C
25 cm
SRX W V
U
T
5x "4x "
(10y # 10)"
B DA
C
EF
50"
B:
Chapter 1 Test, Form 2A11
© Glencoe/McGraw-Hill 39 Glencoe Geometry
Ass
essm
ents
Write the letter for the correct answer in the blank at the right of each question.
1. How many planes can be drawn through any three noncollinear points?A. 0 B. 1 C. 2 D. 3
For Questions 2 and 3, use the figure at the right.
2. Which three points in the figure are collinear?A. A, B, D B. E, C, AC. A, B, C D. F, E, G
3. Name the intersection of the plane P and the plane that contains points B, C, and D.A. point B B. B!D!C. BC!"# D. triangle BCD
4. Find the length of R!S!.
A. 1"156" in. B. 1"
38" in.
C. 1"176" in. D. 1"
58" in.
5. Find the precision for a measurement of 18"12" feet.
A. "12" ft B. "
14" ft C. "
18" ft D. 1 in.
6. Find the length of P!Q!.A. 50.9 cm B. 46.3 cmC. 25.7 cm D. 21.3 cm
7. Find y if B is between A and C, AB is 2y, BC is 6y, and AC is 48.A. 24 B. 8 C. 6 D. 4
8. Find the distance between P(2, 8) and Q(5, 3).A. 9 B. %18! C. %34! D. %170!
9. Find the coordinates of the midpoint of L!B! if L(8, 5) and B(!6, 2).
A. "1, 3"12"# B. "2, 1"
12"# C. "7, 3"
12"# D. "7, 1"
12"#
10. Find the coordinates of T given that S is the midpoint of R!T!, R(!4, 2),and S(6, 8).A. (!14, !4) B. (16, 14) C. (2, 10) D. (1, 5)
P R
38.3 cm
12.6 cmQ
1 2in.
R S
PAB
CE
F
D
G
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
NAME DATE PERIOD
SCORE
© Glencoe/McGraw-Hill 40 Glencoe Geometry
Chapter 1 Test, Form 2A (continued)11
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
For Questions 11 and 12, use the figure at the right.
11. What type of angle is !ABC?A. acute angle B. right angleC. obtuse angle D. straight angle
12. Use a protractor to measure the angles in the figure.Which segment is an angle bisector?A. G!E! B. B!C! C. E!D! D. E!F!
For Questions 13–17, use the figure at the right.
13. Find m!FBD if !FBD and !DBE are complementary and m!FBD is twice m!DBE.A. 30 B. 45C. 60 D. 90
14. Which pair of angles are supplementary?A. !ABE, !CBD B. !ABC, !ABD C. !ABC, !CBD D. !ABC, !EBD
15. Which angle is a vertical angle to !ABE?A. !DBE B. !CBD C. !ABC D. !EBA
16. If m!CBF # 6x $ 18, find x so that CB ! BF.A. 90 B. 45 C. 18 D. 12
17. Find m!ABC if m!ABC # 4x $ 9 and m!EBD # 7x ! 9.A. 6 B. 33 C. 45 D. 73
For Questions 18 and 19, use the figure at the right.
18. Which describes this figure?A. hexagon, concave, not regularB. pentagon, concave, regularC. hexagon, convex, not regularD. not a polygon
19. What is x for a perimeter of 108 kilometers?A. 53 B. 15 C. 18 D. 105
20. A rectangle has a length of 1.4 feet and a width of 1.2 feet. What is the effecton the perimeter of this rectangle if the length and width are doubled?A. The perimeter is doubled. B. The perimeter is increased by 8.C. The perimeter is multiplied by 4. D. The perimeter is tripled.
Bonus Find m!A if !A is complementary to !B, !B is supplementary to !C, m!B # 15x ! 2, and m!C # 25x $ 22.
(x # 3) km
F
DE
B
AC
A B
C
DE
F
G
B:
NAME DATE PERIOD
Chapter 1 Test, Form 2B11
© Glencoe/McGraw-Hill 41 Glencoe Geometry
Ass
essm
ents
Write the letter for the correct answer in the blank at the right of each question.
1. Suppose A and B are points. How many lines contain both A and B?A. 0 B. 1C. 2 D. 3
For Questions 2 and 3, use the figure at the right.
2. Which three points in the figure are collinear?A. C, D, F B. B, C, DC. A, E, F D. A, D, E
3. Name the intersection of the plane that containspoints A, B, and D and the plane P.A. point D B. A!D!C. triangle BCD D. BD!"#
4. Find the length of X!Y!.
A. 1"1116" in. B. 1"
58" in.
C. 1"196" in. D. 1"
12" in.
5. Find the precision for a measurement of 34.0 centimeters.A. 0.5 cm B. 1 mm C. 0.5 mm D. 1 cm
6. Find the length of H!J!.A. 11.3 cm B. 12.3 cmC. 13.7 cm D. 45.9 cm
7. Find x if S is between R and T, RS is x $ 3, ST is 5x, and RT is 57.A. 9 B. 10 C. 10.8 D. 12
8. Find the distance between M(!2, 3) and N(8, 2).
A. 8 B. %61! C. 10 D. %101!
9. Find the coordinates of the midpoint of A!S! if A(!4, 7) and S(5, 3).
A. (1, 10) B. "!4"12", 2# C. ""
12", 5# D. "!"
12", 5#
10. Find the coordinates of T given that S is the midpoint of R!T!, R(2, 6),and S(!2, 0).A. (6, 12) B. (!6, !6) C. (0, 3) D. (!2, 3)
G J
29.1 cm
16.8 cm H
1 2in.
X Y
PCB
D
E
F
A
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
NAME DATE PERIOD
SCORE
© Glencoe/McGraw-Hill 42 Glencoe Geometry
Chapter 1 Test, Form 2B (continued)11
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
For Questions 11 and 12, use the figure at the right.
11. What type of angle is !BAC?A. acute angle B. right angleC. obtuse angle D. straight angle
12. Use a protractor to measure the angles in the figure.Which segment is an angle bisector?A. A!B! B. C!D! C. C!B! D. A!E!
For Questions 13–17, use the figure at the right.
13. Find m!VSW if !WSR and !VSW are complementaryand m!WSR is four times m!VSW.A. 72 B. 36C. 22.5 D. 18
14. Which pair of angles are supplementary?A. !USV, !VSW B. !VSW, !WSR C. !TSV, !VSW D. !TSR, !USW
15. Which angle is a vertical angle to !UST?A. !VSW B. !USV C. !TSR D. !WSR
16. If m!VSR # 8x $ 18, find x so that U!S! ! V!S!.A. 9 B. 12.25 C. 72 D. 90
17. Find m!USW if m!USW # 7x ! 34 and m!TSR # 4x $ 29.A. 147 B. 113 C. 84 D. 21
For Questions 18 and 19, use the figure at the right.
18. Which describes this figure?A. hexagon, convex, regularB. pentagon, concave, regularC. pentagon, convex, not regularD. not a polygon
19. What is y for a perimeter of 100 feet?A. 5 B. 15 C. 17 D. 23
20. A square has sides with a length of 5.8 inches. What is the effect on theperimeter of this square if the sides are tripled?A. The perimeter stays the same. B. The perimeter is increased by 12.C. The perimeter is multiplied by 3. D. The perimeter is multiplied by 9.
Bonus Find m!A if !A is supplementary to !B, !B is supplementary to !C, m!B # 12x $ 8, and m!C # 8x ! 8.
y # 5
y
R
T
U
V W
S
FE
D
CA
B
B:
NAME DATE PERIOD
Chapter 1 Test, Form 2C11
© Glencoe/McGraw-Hill 43 Glencoe Geometry
Ass
essm
ents
For Questions 1–4, use the figure at the right.
1. What is another name for line !?
2. Name three points on plane P.
3. Name the intersection of planes P and N.
4. Name three noncoplanar points.
For Questions 5 and 6,use the figure at theright.
5. What is the length ofA!B!?
6. What is the precision of your measurement of A!B!?
7. Find the length of D!E! if D is between points C and E,CD # 6.5 centimeters, and CE # 13.8 centimeters.
8. Find the length of X!Z!.
9. Find x if R!S! $ S!T!.
For Questions 10–12, use the coordinate grid.
10. Find the distance between A and B.
11. Find the coordinates of the midpoint of C!D!.
12. Find the coordinates of a point E if Cis the midpoint of A!E!.
13. The vertices of a triangle are located at P(0, 0), Q(8, 6), andR(!3, 4). What is the perimeter of this triangle?
14. Find x and y if U!V! bisects T!W! and UV # 40.
ZT W
U
V
3y ! 1
2y # 6
3y # 13x ! 2
x
y
O
B
D
A
C
R T
52 in.
6x # 8 S
X Z
4x # 3
2x # 78 cm Y
1cm 2 3 4 5 6
A B
!
P
N
CA B
DE
F
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
NAME DATE PERIOD
SCORE
© Glencoe/McGraw-Hill 44 Glencoe Geometry
Chapter 1 Test, Form 2C (continued)11
15.
16.
17.
18.
19.
20.
21.
22.
23.
24.
25.
B:
15. Measure !PQR. Then classify !PQRas right, acute, or obtuse.
In the figure, EA!!" and EB!!" are opposite rays and EC!!" bisects !FEG.
16. Find x if m!FEG # 82, and m!FEC # 5x $ 11.
17. If m!AED # 16y $ 10, find y so that E!D! ! A!B!.
For Questions 18–21, use the figure at the right.
18. Find y.
19. Find m!1.
20. Find m!2.
21. Find x .
For Questions 22–25, use the polygons at the right.
22. Name polygon ABCDEF by its sides. Then classify it asconvex or concave and regular or not regular.
23. Find the perimeter of polygon ABCDEF for x # 4.
24. Find the length of each side of polygon RST.
25. Find the length of one side of a regular pentagon whoseperimeter is the same as the perimeter of RST.
Bonus Find the dimensions of a rectangle whose length is 3 more than twice its width and has a perimeter of 30 centimeters.
6x # 53y ! 1
2y # 11
A D
B C R
F E T S
40"
72"1
2
(11x ! 24)"
(8y ! 16)"
BAD
GC
F
E
R
P
Q
NAME DATE PERIOD
Chapter 1 Test, Form 2D11
© Glencoe/McGraw-Hill 45 Glencoe Geometry
Ass
essm
ents
For Questions 1–4, use the figure at the right.
1. What is another name for line m?
2. Name three points on plane B.
3. Name the intersection of planes A and B.
4. Name three noncollinear points.
For Questions 5 and 6, use the figure at the right.
5. What is the length of Q!R!?
6. What is the precision of your measurement of Q!R!?
7. Find the length of L!O! if O is between points L and M,LM # 18.6 centimeters, and OM # 12.9 centimeters.
8. Find the length of D!E!.
9. Find y if X!Y! $ Y!Z!.
For Questions 10–12, use the coordinate grid.
10. Find the distance between Land M.
11. Find the coordinates of the midpoint of M!N!.
12. Find the coordinates of a point Q if P is the midpoint of N!Q!.
13. The vertices of a triangle are located at P(0, 6), Q(8, 12), andR(3, !3). What is the perimeter of this triangle?
14. Find x if R!S! bisects A!B! and RS # 36.
TA B
R
S
18
2y ! 6
2y ! 525 ! 3x
x
y
O
M
NPL
X Z
5y # 11
23 in. Y
D F
24 cm
5x ! 133x # 5 E
1 2in.
Q R
A
B
m
T
R
SU
YZ
X
V
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
NAME DATE PERIOD
SCORE
© Glencoe/McGraw-Hill 46 Glencoe Geometry
Chapter 1 Test, Form 2D (continued)11
15.
16.
17.
18.
19.
20.
21.
22.
23.
24.
25.
B:
15. Measure !ABC. Then classify !ABC as right, acute, or obtuse.
In the figure, RC!!" and RD!!" are opposite rays and RQ!!" bisects !WRV.
16. Find y if m!WRQ # 48 and m!QRV # 7y $ 6.
17. Find x so that C!R! ! P!R!.
For Questions 18–21, use the figure at the right.
18. Find x.
19. Find m!1.
20. Find m!2.
21. Find y.
For Questions 22–25, use the polygons at the right.
22. Name polygon RSTUVby its sides. Then classify it as convex orconcave and regular or not regular.
23. Find the perimeter of polygon RSTUV for y # 9.
24. Find the length of each side of polygon ABCD.
25. Find the length of the sides of a regular triangle whoseperimeter is the same as the perimeter of ABCD.
Bonus Find the lengths of the sides of a triangle whose perimeter is 37. The measure of the first side of thetriangle is 8 less than the second side, and the second side is twice the length of the third side.
5y ! 8
8x # 3
27 # 4x
S
R T
U D C
A B
V
(9x ! 5)" 58"1
2(7y # 27)"
DR
P
C
WQ V
(13x # 12)"
C
A
B
NAME DATE PERIOD
Chapter 1 Test, Form 311
© Glencoe/McGraw-Hill 47 Glencoe Geometry
Ass
essm
ents
For Questions 1–3, use the figure at the right.
1. Name five planes shown in the figure.
2. Name a line that is coplanar with AD!"# and AB!"#.
3. Name the intersection of plane P and the plane that containspoints A, B, and E.
For Questions 4 and 5, usethe figure at the right.
4. Find the length of A!B!.
5. Find the precision for the measurement of A!B!.
6. Find two possible lengths for C!D! if C, D, and E are collinear,CE # 15.8 centimeters, and DE # 3.5 centimeters.
7. Find the length of R!S! if S is between R and T, the length of R!S! is "
13" the length of R!T!, RS # 3x ! 3, and ST # 2x $ 6.
8. Find y if AC # 3y $ 5, CB # 4y ! 1, AB # 9y ! 12, and pointC lies between A and B.
For Questions 9–11, use the coordinate grid at the right.
9. Find the distance between A and B.
10. Find two possible coordinates of a point D on a line containing A!B! so that AD # "
14"AB.
11. Find two values of y for C located at (1, y) and AC # 5.
x
y
O
B
A
6 7in.
A B
P
A
E
F
D
C
B
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
NAME DATE PERIOD
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© Glencoe/McGraw-Hill 48 Glencoe Geometry
Chapter 1 Test, Form 3 (continued)11
12.
13.
14.
15.
16.
17.
18.
19.
20.
B:
12. Find y if S is the midpoint of R!T!, T is the midpoint of R!U!,RS # 6x $ 5, ST # 8x ! 1, and TU # 11y $ 13.
13. Find all values of x that will make !A an obtuse angle givenm!A # 12x ! 6.
14. Find m!RST if ST""# bisects !RSU and SU""# bisects !TSV.
15. Find m!1 if !1 is complementary to !2, !2 is supplementaryto !3, and m!3 # 126.
16. Find y if XW""# ! XZ""#, Y is in the interior of !WXZ,m!WXY # 6y ! 3, and m!YXZ # 4y $ 13.
17. Find the length of L!M! if ON!"# is the bisector of L!M! and LN # 3x $ 2.
For Questions 18 and 19, use the coordinate grid.
18. Graph polygon ABCD with vertices A(4, 3), B(0, 3), C(!2, 2),and D(!5, 6). Then name polygon ABCD by its number ofsides and classify it as convex or concave and regular orirregular.
19. Find the perimeter of polygon ABCD.
20. Find the perimeter of regular triangle DEF if DE # 28 ! 3yand EF # 2y $ 3.
Bonus Suppose a regular quadrilateral and a regular triangle havethe same perimeter. The sides of the triangle are 3 incheslonger than the sides of the quadrilateral. Find the lengthsof the sides of the quadrilateral and the triangle.
N ML
O
7x ! 1
V
U
T
R
S
(x # 2y ! 1)"
(6x ! 9)"
(2y # 5)"
NAME DATE PERIOD
Chapter 1 Open-Ended Assessment11
© Glencoe/McGraw-Hill 49 Glencoe Geometry
Ass
essm
ents
Demonstrate your knowledge by giving a clear, concise solution toeach problem. Be sure to include all relevant drawings and justifyyour answers. You may show your solution in more than one way orinvestigate beyond the requirements of the problem.
1. Draw and label a figure that shows that plane R contains both lines s andAC!"# that intersect at point B. Name three collinear points in plane R.
2. Draw a line on a coordinate plane so that you can determine at least twopoints on the graph. Label those two points D and G.
a. Find the distance between points D and G.
b. Find the coordinates of E, the midpoint of D!G!.
c. Find the coordinates of point H given that G is the midpoint of D!H!.
3. Rectangle WXYZ has a length that is 5 more than three times its width.
a. Draw and label a figure for rectangle WXYZ.
b. Write an algebraic expression for the perimeter of the rectangle.
c. Find the width if the perimeter is 58 millimeters. Explain how you cancheck that your answer is correct.
d. Use a ruler to draw and label P!Q!, which is congruent to the segmentrepresenting the length of rectangle WXYZ. What is the measure of P!Q!?
e. Explain how to find the precision of the measurement of P!Q!.
4. Draw an acute angle, !ABC. Let m!ABC # 6x ! 1.
a. Use a protractor to determine the measure of !ABC. Use thismeasure to determine the value of x.
b. Explain how you would determine the measure of an angle that iscomplementary to !ABC.
c. Explain how you would determine the measure of an angle that issupplementary to !ABC.
5. RS""# is in the interior of !TRU, m!TRS # 4x $ 6, and m!SRU # 8x ! 6.
a. Draw !TRU and RS""#.
b. Determine the value of x that will make RS""# an angle bisector. Explainyour steps.
c. Describe the relationship between RU""# and RT""# when x # 7.5.
NAME DATE PERIOD
SCORE
© Glencoe/McGraw-Hill 50 Glencoe Geometry
Chapter 1 Vocabulary Test/Review11
Choose from the terms above to complete each sentence.
1. Two lines are if they intersect to form a right angle.
2. Two angles are if their measures have a sum of 90°.
3. When two rays intersect with a common endpoint a(n) is formed.
4. The is the point located halfway between theendpoints of a segment.
5. are nonadjacent angles formed by the intersection oftwo lines.
6. A(n) divides an angle into two congruent angles.
7. Two angles are if their measures have a sum of 180°.
8. Two angles that lie in the same plane are called ifthey share a common side and a common vertex.
9. A(n) is an angle whose measure is less than 90°.
10. Two segments are if they have the same measure.
In your own words—
11. Explain how to find the precision of a measurement of 5"
12" inches on a ruler marked in half inches.
12. Describe what is meant by betweenness of points usingcollinear points M, P, and Q.
?
?
?
?
?
?
?
?
?
? 1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
acute angleadjacent anglesangleangle bisectorbetweenness collinearcomplementary concavecongruentconstruction
convexcoplanardegreedistanceexteriorinteriorlineline segmentlinear pairmidpoint
n-gonobtuse angleopposite raysperimeterperpendicularplanepointpolygonprecisionray
regular polygonrelative errorright anglesegment bisectorsidesspacesupplementaryundefined termsvertexvertical angles
NAME DATE PERIOD
SCORE
Chapter 1 Quiz (Lessons 1–1 and 1–2)
11
© Glencoe/McGraw-Hill 51 Glencoe Geometry
Ass
essm
ents
NAME DATE PERIOD
SCORE
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
For Questions 1–3, use the figure at the right.
1. What is another name for line !?
2. Name the intersection of lines ! and m.
3. Name three collinear points.
For Questions 4 and 5, use the figure at the right.
4. Find the length of A!B!.
5. Find the precision of the measurement of A!B!.
6. Find the length of U!W! if W is between U and V,UV # 16.8 centimeters, and VW # 7.9 centimeters.
7. Find x if RS # 24 centimeters.
8. Find the length of L!O! if M is between L and O, LM # 7x ! 9,MO # 14 inches, and LO # 10x ! 7.
9. Find x if P!Q! $ R!S!, PQ # 9x ! 7, and RS # 29.
10. STANDARDIZED TEST PRACTICE Which of the following isnot an undefined term in geometry?A. plane B. point C. bisector D. line
R S
10 cm6x ! 4
T
1in.
A B
R T
SU
m
!V
Chapter 1 Quiz (Lesson 1–3)
11
1.
2.
3.
4.
5.
1. Find the coordinates of the midpoint of A!B! for A(2, 5) and B(6, 9).
2. Find the coordinates of D if E is the midpoint of C!D!, for C(!3, 4) and E(0, 1).
3. What is the length of F!H! if G is the midpoint, FG # 12x ! 5,and GH # 7x?
4. What is the length of U!V! if WX!"# is the segment bisector of U!V! at point Z?
5. STANDARDIZED TEST PRACTICE Find the distance betweenA(!2, 1) and B(4, !3).A. 52 B. %52! C. %20! D. %8!
U
V9x # 2
6x # 8Z
X
W
NAME DATE PERIOD
SCORE
© Glencoe/McGraw-Hill 52 Glencoe Geometry
Chapter 1 Quiz (Lessons 1–4 and 1–5)
11
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
For Questions 1–6, use the figure at the right.
1. Name the vertex of !1.
2. Classify !TSV as right, acute, or obtuse.
3. Name a point in the exterior of !RTS.
4. Find m!TSU if S!U! bisects !TSV,m!TSU # 4y $ 11, and m!USV # 6y $ 5.
5. Name a pair of adjacent angles.
6. Name a pair of vertical angles.
7. Find m!DBC if m!ABC # 5x $ 3 and !ABD $ !DBC.
For Questions 8 and 9, lines p and q intersect to formadjacent angles 1 and 2.
8. If m!1 # 7x $ 6 and m!2 # 8x ! 6, find x so that p isperpendicular to q.
9. If m!1 # 4x ! 3 and m!2 # 3x $ 8, find x so that !1 issupplementary to !2.
10. STANDARDIZED TEST PRACTICE The difference betweentwo complementary angles is 14. Which is the measure of oneof those angles?A. 14 B. 52 C. 83 D. 90
(3x ! 2)"B
A
DC
ST
U V
W
PR
1
NAME DATE PERIOD
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Chapter 1 Quiz (Lesson 1–6)
11
1.
2.
3.
4.
5.
1. Draw a concave pentagon.
2. Find the length of each side of a regular hexagon whoseperimeter is 84 meters.
3. If x # 5, find the perimeter of the rectangle whose length is 6x ! 4 and whose width is 3x $ 2.
4. The perimeter of a convex pentagon is 15 feet. What is theeffect on its perimeter if each side is doubled?
5. For what value of y is triangle ABC a regular triangle?
7y # 12
5y # 209y # 4
B
CA
NAME DATE PERIOD
SCORE
Chapter 1 Mid-Chapter Test (Lessons 1–1 through 1–3)
11
© Glencoe/McGraw-Hill 53 Glencoe Geometry
Ass
essm
ents
For Questions 1 and 2, use the figure at the right.
1. Which point is coplanar with points A and C?A. A B. BC. C D. D
2. Name the point of intersection of plane M and DE!"#.A. D B. E C. B D. M
For Questions 3 and 4, use the figure at the right.
3. What is the length of A!B!?
A. about 1"14" in. B. about 1"
12" in.
C. about 1"34" in. D. about 2 in.
4. What is the precision for the measurement of A!B!?
A. 1 in. B. "12" in. C. "
14" in. D. "
18" in.
5. What is the length of T!S!?A. 9.4 cm B. 8.9 cmC. 4.7 cm D. 4.2 cm
R S
8.9 cm
4.7 cm T
1 2in.
A B
MBCA
D
E
6.
7.
8.
9.
10.
NAME DATE PERIOD
SCORE
1.
2.
3.
4.
5.
Part IIFor Questions 6–8, use the coordinate grid.
6. Find the distance between R and S.
7. Find the coordinates of the midpoint of T!U!.
8. Find the coordinates of a point M given that U is the midpoint of M!S!.
9. Find y if M is the midpoint of L!N!.
10. In the figure, WZ!"# bisects X!Y!. Find the length of X!Y!.
XY
6x ! 114x # 5
V
Z
W
L N
6y # 59y ! 4
M
x
y
O
R US
T
Part I Write the letter for the correct answer in the blank at the right of each question.
© Glencoe/McGraw-Hill 54 Glencoe Geometry
Chapter 1 Cumulative Review(Chapter 1)
11
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
For Questions 1 and 2, use the figure at the right.
1. Name three points that are collinear.(Lesson 1-1)
2. Name the intersection of AE!"# and CG!"#.(Lesson 1-1)
Find the measurement of each segment. Assume that theart is not drawn to scale. (Lesson 1-2)
3. A!B!
4. K!N!
5. Use the Pythagorean Theorem to find the distance betweenA(!12, 13) and B(!2, !11). (Lesson 1-3)
6. Find the coordinates of B if A has coordinates (3, 5) and Y(!2, 3) is the midpoint of A!B!. (Lesson 1-3)
For Questions 7 and 8, use the figure to name the vertex and sides of each angle. Then measure and classify each angle. (Lesson 1-4)
7. !JNK 8. !HNK
For Questions 9–11, use the figure at the right. (Lesson 1-5)
9. Name a pair of supplementarynonadjacent angles.
10. Name two obtuse vertical angles.
11. Name an angle complementary to !CFD.
12. If m!HJK # 7y ! 2 and m!PQR # 133, find y so that !HJKis supplementary to !PQR. (Lesson 1-5)
13. Name this polygon by its number of sides and then classify it as convex or concave and regularor irregular. (Lesson 1-6)
14. Find the perimeter of "ABC if A(1, 1), B(4, !3), and C(!3, !2).(Lesson 1-6)
15. Find the length of each side of a regular pentagon whoseperimeter is 90 centimeters. (Lesson 1-6)
A F DE
B C
G60" 30"
120"
N
K
M
J
H
L
157"
77"26"
J K L M N
4 mm 3 mm
A C5 cm
2 cmB
A
C
E
B
D
FG
H
NAME DATE PERIOD
SCORE
Standardized Test Practice (Chapter 1)
© Glencoe/McGraw-Hill 55 Glencoe Geometry
1. Which object models a line? (Lesson 1-1)
A. a fly B. a wall C. a meter stick D. a diskette
2. Which figure shows AB!"# and point G contained in plane R ? (Lesson 1-1)
E. F.
G. H.
3. What is the precision of a measurement of 49.5 centimeters on aruler with millimeter marks? (Lesson 1-2)
A. 49 cm to 50 cm B. 49.0 cm to 50.0 cmC. 490 mm to 500 mm D. 494.5 mm to 495.5 mm
4. When segments have the same measure, they are said to be. (Lesson 1-2)
E. accurate F. congruentG. precise H. constructed
5. Find the distance between A(!3, 5) and B(4, 2), to the nearesthundredth. (Lesson 1-3)
A. 6.75 B. 7.62 C. 8.06 D. 10
6. Find EF if E is the midpoint of D!F!, DE # 15 ! 3x, and EF # x $ 3. (Lesson 1-3)
E. 1 F. 3 G. 6 H. 9
For Questions 7–9, use the figure.
7. What is another name for !2? (Lesson 1-4)
A. !WYX B. !WXYC. !3 D. !Y
8. Which angles form a linear pair? (Lesson 1-5)
E. !1 and !3 F. !2 and !5 G. !2 and !3 H. !1 and !4
9. Name the angle that is vertical to !3. (Lesson 1-5)
A. !1 B. !2 C. !3 D. !4
10. Find the length of one side of a regular hexagon whose perimeteris 75 feet. (Lesson 1-6)
E. 25 ft F. 18.75 ft G. 15 ft H. 12.5 ft
WY
X14
235
?
A
B
G RA B
G
R
A BR
GA BG R
NAME DATE PERIOD
SCORE
Part 1: Multiple ChoiceInstructions: Fill in the appropriate oval for the best answer.
1.
2.
3.
4.
5.
6.
7.
8.
9.
10. E F G H
A B C D
E F G H
A B C D
E F G H
A B C D
E F G H
A B C D
E F G H
A B C D
Ass
essm
ents
11
© Glencoe/McGraw-Hill 56 Glencoe Geometry
Standardized Test Practice (continued)
11. How many points name a line? (Lesson 1-1)
12. What is the measure of A!C!? (Lesson 1-2)
For Questions 13–15, HL!!" bisects !KHI andHG!!" and HI!!" are opposite rays.
13. If !1 $ !2, m!KHG # 70, and m!1 # 3d $ 2,find d. (Lesson 1-4)
14. If m!2 # a $ 15 and m!3 # a $ 35, find a sothat HL""# ! HJ""#. (Lesson 1-5)
15. Find m!4, if m!GHL # 125. (Lesson 1-5)
G H I
J
KL
1 42 3
A B C3.7 5.2
NAME DATE PERIOD
Part 2: Grid InInstructions: Enter your answer by writing each digit of the answer in a column boxand then shading in the appropriate oval that corresponds to that entry.
Part 3: Short ResponseInstructions: Show your work or explain in words how you found your answer.
11. 12.
13. 14.
15.
0 0 0
.. ./ /
.
99 9 987654321
87654321
87654321
87654321
0 0 0
.. ./ /
.
99 9 987654321
87654321
87654321
87654321
0 0 0
.. ./ /
.
99 9 987654321
87654321
87654321
87654321
0 0 0
.. ./ /
.
99 9 987654321
87654321
87654321
87654321
0 0 0
.. ./ /
.
99 9 987654321
87654321
87654321
87654321
16. Find the length of X!Z! if Y(!4, 4) is the midpoint of X!Z! and X has coordinates (2, !4). (Lesson 1-3)
17. Find the perimeter of this hexagon.(Lesson 1-6)
18. Find the measure of W!X!, if the perimeter of pentagon UVWXY is 48 units. (Lesson 1-6)
10 ! a
2aW X
UV Y
4a # 7
30 m
20 m
7 m 6 m
10 m8.5 m
16.
17.
18.
2 8 . 9
1 1
5 5
2 0
11
Standardized Test PracticeStudent Record Sheet (Use with pages 58–59 of the Student Edition.)
11
© Glencoe/McGraw-Hill A1 Glencoe Geometry
An
swer
s
Select the best answer from the choices given and fill in the corresponding oval.
1 4 7
2 5 8
3 6 9 DCBADCBADCBA
DCBADCBADCBA
DCBADCBADCBA
NAME DATE PERIOD
Part 1 Multiple ChoicePart 1 Multiple Choice
Part 2 Short Response/Grid InPart 2 Short Response/Grid In
Part 3 Open-EndedPart 3 Open-Ended
Solve the problem and write your answer in the blank.
For Questions 14 and 15, also enter your answer by writing each number orsymbol in a box. Then fill in the corresponding oval for that number or symbol.
10 14 15
11
12
13
14 (grid in)
15 (grid in)
0 0 0
.. ./ /
.
99 9 987654321
87654321
87654321
87654321
0 0 0
.. ./ /
.
99 9 987654321
87654321
87654321
87654321
Record your answers for Questions 16–17 on the back of this paper.
© Glencoe/McGraw-Hill A2 Glencoe Geometry
Stu
dy
Gu
ide
and I
nte
rven
tion
Poin
ts,L
ines
,and
Pla
nes
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
PE
RIO
D__
___
1-1
1-1
©G
lenc
oe/M
cGra
w-H
ill1
Gle
ncoe
Geo
met
ry
Lesson 1-1
Nam
e Po
ints
, Lin
es, a
nd
Pla
nes
In g
eom
etry
,a p
oin
tis
a lo
cati
on,a
lin
eco
ntai
nspo
ints
,and
a p
lan
eis
a f
lat
surf
ace
that
con
tain
s po
ints
and
line
s.If
poi
nts
are
on t
he s
ame
line,
they
are
col
lin
ear.
If p
oint
s on
are
the
sam
e pl
ane,
they
are
cop
lan
ar.
Use
th
e fi
gure
to
nam
e ea
ch o
f th
e fo
llow
ing.
a.a
lin
e co
nta
inin
g p
oin
t A
The
line
can
be
nam
ed a
s !.
Als
o,an
y tw
o of
the
thr
ee
poin
ts o
n th
e lin
e ca
n be
use
d to
nam
e it
.
AB
!"# ,
AC
!"# ,
or B
C!"
#
b.a
pla
ne
con
tain
ing
poi
nt
D
The
pla
ne c
an b
e na
med
as
plan
e N
or c
an b
e na
med
usi
ng t
hree
no
ncol
linea
r po
ints
in t
he p
lane
,suc
h as
pla
ne A
BD
,pla
ne A
CD
,and
so
on.
Ref
er t
o th
e fi
gure
.
1.N
ame
a lin
e th
at c
onta
ins
poin
t A
.A
B!"
# ,A
C!"
# ,B
C!"
# ,or
!
2.W
hat
is a
noth
er n
ame
for
line
m?
BD
!"#
3.N
ame
a po
int
not
on A
C!"
# .D
or E
4.N
ame
the
inte
rsec
tion
of
AC
!"#
and
DB
!"# .
B
5.N
ame
a po
int
not
on li
ne !
or li
ne m
.E
Dra
w a
nd
lab
el a
pla
ne
Qfo
r ea
ch r
elat
ion
ship
.
6.A
B!"
#is
in p
lane
Q.
7.S
T!"
#in
ters
ects
AB
!"#
at P
.
8.Po
int
Xis
col
linea
r w
ith
poin
ts A
and
P.
Ans
wer
s fo
r E
xerc
ises
6–1
0
9.Po
int
Yis
not
col
linea
r w
ith
poin
ts T
and
P.
10.L
ine
!co
ntai
ns p
oint
s X
and
Y.
!Q
AB
S P
TY
X
!
PmA
B EC
D
!
N
AB
C
DExam
ple
Exam
ple
Exercis
esExercis
es
©G
lenc
oe/M
cGra
w-H
ill2
Gle
ncoe
Geo
met
ry
Poin
ts, L
ines
, an
d P
lan
es in
Sp
ace
Sp
ace
is a
bou
ndle
ss,t
hree
-dim
ensi
onal
set
of
all p
oint
s.It
con
tain
s lin
es a
nd p
lane
s.
a.H
ow m
any
pla
nes
ap
pea
r in
th
e fi
gure
?
The
re a
re t
hree
pla
nes:
plan
e N
,pla
ne O
,and
pla
ne P
.
b.A
re p
oin
ts A
,B,a
nd
Dco
pla
nar
?
Yes.
The
y ar
e co
ntai
ned
in p
lane
O.
Ref
er t
o th
e fi
gure
.
1.N
ame
a lin
e th
at is
not
con
tain
ed in
pla
ne N
.A
B!"
#
2.N
ame
a pl
ane
that
con
tain
s po
int
B.
plan
e N
,pla
ne A
BC
,pla
ne A
BD
,pla
ne E
BC
,pl
ane
EB
D3.
Nam
e th
ree
colli
near
poi
nts.
A,B
,E
Ref
er t
o th
e fi
gure
.
4.H
ow m
any
plan
es a
re s
how
n in
the
fig
ure?
6
5.A
re p
oint
s B
,E,G
,and
Hco
plan
ar?
Exp
lain
.N
o;B
,G,a
nd H
lie in
pla
ne B
GH
,but
Edo
es n
ot.
6.N
ame
a po
int
copl
anar
wit
h D
,C,a
nd E
.F
or J
Dra
w a
nd
lab
el a
fig
ure
for
eac
h r
elat
ion
ship
.
7.P
lane
s M
andN
inte
rsec
t in
HJ
!"# .
8.L
ine
ris
in p
lane
N,l
ine
sis
in p
lane
M,a
nd li
nes
rand
sin
ters
ect
at p
oint
J.
9.L
ine
tco
ntai
ns p
oint
Han
d lin
e td
oes
not
lie in
pla
ne M
orpl
ane
N.
Ans
wer
s fo
r E
xerc
ises
7–9
N
Ms
t
r
HJ
AB C
D
EFG
HI
J
N
A
C
B
DE
NO
P
AB
CD
Stu
dy
Gu
ide
and I
nte
rven
tion
(con
tinu
ed)
Poin
ts,L
ines
,and
Pla
nes
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
PE
RIO
D__
___
1-1
1-1
Exam
ple
Exam
ple
Exercis
esExercis
es
Answers (Lesson 1-1)
© Glencoe/McGraw-Hill A3 Glencoe Geometry
An
swer
s
Skil
ls P
ract
ice
Poin
ts,L
ines
,and
Pla
nes
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
PE
RIO
D__
___
1-1
1-1
©G
lenc
oe/M
cGra
w-H
ill3
Gle
ncoe
Geo
met
ry
Lesson 1-1
Ref
er t
o th
e fi
gure
.
1.N
ame
a lin
e th
at c
onta
ins
poin
t D
.
por
CD
!"#
2.N
ame
a po
int
cont
aine
d in
line
n.
Aor
B
3.W
hat
is a
noth
er n
ame
for
line
p?C
D!"
#or
DC
!"#
4.N
ame
the
plan
e co
ntai
ning
line
s n
and
p.S
ampl
e an
swer
:pla
ne G
Dra
w a
nd
lab
el a
fig
ure
for
eac
h r
elat
ion
ship
.S
ampl
e an
swer
s ar
e gi
ven.
5.Po
int
Klie
s on
RT
!"# .
6.P
lane
Jco
ntai
ns li
ne s.
7.Y
P! "
#lie
s in
pla
ne B
and
cont
ains
8.
Lin
es q
and
fint
erse
ct a
t po
int
Zpo
int
C,b
ut d
oes
not
cont
ain
poin
t H
.in
pla
ne U
.
Ref
er t
o th
e fi
gure
.
9.H
ow m
any
plan
es a
re s
how
n in
the
fig
ure?
5
10.H
ow m
any
of t
he p
lane
s co
ntai
n po
ints
Fan
d E
?
2
11.N
ame
four
poi
nts
that
are
cop
lana
r.
A,B
,E,F
or B
,C,D
,Eor
A,C
,D,F
12.A
re p
oint
s A
,B,a
nd C
copl
anar
? E
xpla
in.
Yes;
poin
ts A
,B,a
nd C
lie in
pla
ne W
.
WA
BE
CDF
U
qf
Z
HP
B
CY
J
sT
RK
Gn
AB
D
C
p
©G
lenc
oe/M
cGra
w-H
ill4
Gle
ncoe
Geo
met
ry
Ref
er t
o th
e fi
gure
.
1.N
ame
a lin
e th
at c
onta
ins
poin
ts T
and
P.
g,TP!"
# ,TN!"
# ,N
P!"
#
2.N
ame
a lin
e th
at in
ters
ects
the
pla
ne c
onta
inin
g po
ints
Q,N
,and
P.
jor
MT
!"#
3.N
ame
the
plan
e th
at c
onta
ins
TN
!"#
and
QR
!"# .
Sam
ple
answ
er:p
lane
S
Dra
w a
nd
lab
el a
fig
ure
for
eac
h r
elat
ion
ship
.S
ampl
e an
swer
s ar
e gi
ven.
4.A
K!"
#an
d C
G!"
#in
ters
ect
at p
oint
M5.
A li
ne c
onta
ins
L(!
4,!
4) a
nd M
(2,3
).L
ine
in p
lane
T.
q is
in t
he s
ame
coor
dina
te p
lane
but
doe
sno
t in
ters
ect
LM
!"# .
Lin
e q
cont
ains
poi
nt N
.
Ref
er t
o th
e fi
gure
.
6.H
ow m
any
plan
es a
re s
how
n in
the
fig
ure?
6
7.N
ame
thre
e co
lline
ar p
oint
s.S
,X,M
8.A
re p
oint
s N
,R,S
,and
Wco
plan
ar?
Exp
lain
.N
o;sa
mpl
e an
swer
:poi
nts
N,R
,and
Slie
in
pla
ne A
,but
poi
nt W
doe
s no
t.
VIS
UA
LIZA
TIO
NN
ame
the
geom
etri
c te
rm(s
) m
odel
ed b
y ea
ch o
bjec
t.
9.10
.11
.
plan
e an
d lin
epo
int
lines
12.a
car
ant
enna
13.a
libr
ary
card
line
and
poin
tpl
ane
strin
gs
tip o
f pin
STOP
AM
N
PW
S XRQ
T
L
M
N
q
x
y
O
KT
M
C
GA
S
j
ghTM
NQ
R
P
Pra
ctic
e (A
vera
ge)
Poin
ts,L
ines
,and
Pla
nes
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
PE
RIO
D__
___
1-1
1-1
Answers (Lesson 1-1)
© Glencoe/McGraw-Hill A4 Glencoe Geometry
Rea
din
g t
o L
earn
Math
emati
csPo
ints
,Lin
es,a
nd P
lane
s
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
PE
RIO
D__
___
1-1
1-1
©G
lenc
oe/M
cGra
w-H
ill5
Gle
ncoe
Geo
met
ry
Lesson 1-1
Pre-
Act
ivit
yW
hy
do
chai
rs s
omet
imes
wob
ble?
Rea
d th
e in
trod
ucti
on t
o L
esso
n 1-
1 at
the
top
of
page
6 in
you
r te
xtbo
ok.
•F
ind
thre
e pe
ncils
of
diff
eren
t le
ngth
s an
d ho
ld t
hem
upr
ight
on
your
desk
so
that
the
thr
ee p
enci
l poi
nts
do n
ot li
e al
ong
a si
ngle
line
.Can
you
plac
e a
flat
she
et o
f pa
per
or c
ardb
oard
so
that
it t
ouch
es a
ll th
ree
penc
ilpo
ints
?ye
s•
How
man
y w
ays
can
you
do t
his
if y
ou k
eep
the
penc
il po
ints
in t
he s
ame
posi
tion
?on
e•
How
will
you
r an
swer
cha
nge
if t
here
are
fou
r pe
ncil
poin
ts?
Sam
ple
answ
er:I
t m
ay n
ot b
e po
ssib
le t
o pl
ace
the
pape
r to
tou
chal
l fou
r po
ints
.
Rea
din
g t
he
Less
on
1.C
ompl
ete
each
sen
tenc
e.
a.Po
ints
tha
t lie
on
the
sam
e lie
are
cal
led
poin
ts.
b.Po
ints
tha
t do
not
lie
in t
he s
ame
plan
e ar
e ca
lled
poin
ts.
c.T
here
is e
xact
ly o
ne
thro
ugh
any
two
poin
ts.
d.T
here
is e
xact
ly o
ne
thro
ugh
any
thre
e no
ncol
linea
r po
ints
.
2.R
efer
to
the
figu
re a
t th
e ri
ght.
Indi
cate
whe
ther
eac
h st
atem
ent
is t
rue
or f
alse
.
a.Po
ints
A,B
,and
Car
e co
lline
ar.
fals
e
b.T
he in
ters
ecti
on o
f pl
ane
AB
Can
d lin
e m
is p
oint
P.
true
c.L
ine
!an
d lin
e m
do n
ot in
ters
ect.
fals
e
d.Po
ints
A,P
,and
Bca
n be
use
d to
nam
e pl
ane
U.
fals
e
e.L
ine
!lie
s in
pla
ne A
CB
.tr
ue
3.C
ompl
ete
the
figu
re a
t th
e ri
ght
to s
how
the
fol
low
ing
rela
tion
ship
:Lin
es !
,m,a
nd n
are
copl
anar
and
lie
in
plan
e Q.
Lin
es !
and
min
ters
ect
at p
oint
P.L
ine
nin
ters
ects
line
mat
R,b
ut d
oes
not
inte
rsec
t lin
e !.
Hel
pin
g Y
ou
Rem
emb
er
4.R
ecal
l or
look
in a
dic
tion
ary
to f
ind
the
mea
ning
of
the
pref
ix c
o-.W
hat
does
thi
s pr
efix
mea
n? H
ow c
an it
hel
p yo
u re
mem
ber
the
mea
ning
of c
olli
near
?S
ampl
e an
swer
:The
pre
fix c
o-m
eans
toge
ther
.The
wor
d co
lline
arco
ntai
ns t
he w
ord
line,
so c
ollin
ear
mea
ns to
geth
er o
n a
line.
Qn
m
!P
R
U
m
!P
C
D
B
A
plan
e
line
nonc
opla
nar
colli
near
©G
lenc
oe/M
cGra
w-H
ill6
Gle
ncoe
Geo
met
ry
Poin
ts a
nd L
ines
on
a M
atri
xA
mat
rix
is a
rec
tang
ular
arr
ay o
f ro
ws
and
colu
mns
.Poi
nts
and
lines
on
a m
atri
x ar
e no
t de
fine
d in
the
sam
e w
ay a
s in
Euc
lidea
nge
omet
ry.A
poi
nt
on a
mat
rix
is a
dot
,whi
ch c
an b
e sm
all o
rla
rge.
A l
ine
on a
mat
rix
is a
pat
h of
dot
s th
at “
line
up.”
Bet
wee
ntw
o po
ints
on
a lin
e th
ere
may
or
may
not
be
othe
r po
ints
.Thr
eeex
ampl
es o
f lin
es a
re s
how
n at
the
upp
er r
ight
.The
bro
ad li
ne c
anbe
tho
ught
of
as a
sin
gle
line
or a
s tw
o na
rrow
line
s si
de b
y si
de.
Dot
-mat
rix
prin
ters
for
com
pute
rs u
sed
dots
to
form
cha
ract
ers.
The
dot
s ar
e of
ten
calle
d p
ixel
s.T
he m
atri
x at
the
rig
ht s
how
sho
w a
dot
-mat
rix
prin
ter
mig
ht p
rint
the
lett
er P
.
Ans
wer
s m
ay v
ary.
Sam
ple
answ
ers
are
show
n.D
raw
poi
nts
on
eac
h m
atri
x to
cre
ate
the
give
n f
igu
res.
1.D
raw
tw
o in
ters
ecti
ng li
nes
that
hav
e2.
Dra
w t
wo
lines
tha
t cr
oss
but
have
fo
ur p
oint
s in
com
mon
.no
com
mon
poi
nts.
3.M
ake
the
num
ber
0 (z
ero)
so
that
it4.
Mak
e th
e ca
pita
l let
ter
O s
o th
at it
exte
nds
to t
he t
op a
nd b
otto
m s
ides
exte
nds
to e
ach
side
of
the
mat
rix.
of t
he m
atri
x.
5.U
sing
sep
arat
e gr
id p
aper
,mak
e do
t de
sign
s fo
r se
vera
l oth
er le
tter
s.W
hich
wer
e th
eea
sies
t an
d w
hich
wer
e th
e m
ost
diff
icul
t?S
ee s
tude
nts’
wor
k.
En
rich
men
t
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
PE
RIO
D__
___
1-1
1-1
Answers (Lesson 1-1)
© Glencoe/McGraw-Hill A5 Glencoe Geometry
An
swer
s
Stu
dy
Gu
ide
and I
nte
rven
tion
Line
ar M
easu
re a
nd P
reci
sion
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
PE
RIO
D__
___
1-2
1-2
©G
lenc
oe/M
cGra
w-H
ill7
Gle
ncoe
Geo
met
ry
Lesson 1-2
Mea
sure
Lin
e Se
gm
ents
A p
art
of a
line
bet
wee
n tw
o en
dpoi
nts
is c
alle
d a
lin
ese
gmen
t.T
he le
ngth
s of
M !N!
and
R!S!
are
wri
tten
as
MN
and
RS
.Whe
n yo
u m
easu
re a
segm
ent,
the
prec
isio
n of
the
mea
sure
men
t is
hal
f of
the
sm
alle
st u
nit
on t
he r
uler
.
Fin
d t
he
len
gth
of
M!N!
.
The
long
mar
ks a
re c
enti
met
ers,
and
the
shor
ter
mar
ks a
re m
illim
eter
s.T
he le
ngth
of
M !N!
is 3
.4 c
enti
met
ers.
The
mea
sure
men
t is
ac
cura
te t
o w
ithi
n 0.
5 m
illim
eter
,so
M !N!
isbe
twee
n 3.
35 c
enti
met
ers
and
3.45
cent
imet
ers
long
.
1cm
23
4
MN
Fin
d t
he
len
gth
of
R!S!.
The
long
mar
ks a
re in
ches
and
the
sho
rt
mar
ks a
re q
uart
er in
ches
.The
leng
th o
f R !S!
is a
bout
1"3 4"
inch
es.T
he m
easu
rem
ent
is
accu
rate
to
wit
hin
one
half
of a
qua
rter
inch
,or
"1 8"in
ch,s
o R!
S!is
bet
wee
n 1"
5 8"in
ches
and
1"7 8"
inch
es lo
ng.1
2in
.
RS
Exam
ple1
Exam
ple1
Exam
ple2
Exam
ple2
Exercis
esExercis
es
Fin
d t
he
len
gth
of
each
lin
e se
gmen
t or
obj
ect.
1.2.
5 cm
2.1!
1 4!in
.
3.2!
1 4!in
.4.
1.7
cm
Fin
d t
he
pre
cisi
on f
or e
ach
mea
sure
men
t.
5.10
in.
6.32
mm
7.44
cm
!1 2!in
.0.
5 m
m0.
5 cm
8.2
ft9.
3.5
mm
10.2
"1 2"yd
!1 2!ft
or
6 in
.0.
05 m
m!1 4!
yd o
r 9
in.
1cm
23
12
in.
1in
.
ST
1cm
23
AB
©G
lenc
oe/M
cGra
w-H
ill8
Gle
ncoe
Geo
met
ry
Cal
cula
te M
easu
res
On
PQ
!"# ,
to s
ay t
hat
poin
t M
is
betw
een
poin
ts P
and
Qm
eans
P,Q
,and
Mar
e co
lline
ar
and
PM
#M
Q$
PQ
.
On
AC
!"# ,
AB
$B
C$
3 cm
.We
can
say
that
the
seg
men
ts a
reco
ngr
uen
t,or
A !B!
"B!
C!.S
lash
es o
n th
e fi
gure
indi
cate
whi
chse
gmen
ts a
re c
ongr
uent
.
AB
CQM
P
Stu
dy
Gu
ide
and I
nte
rven
tion
(con
tinu
ed)
Line
ar M
easu
re a
nd P
reci
sion
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
PE
RIO
D__
___
1-2
1-2
Fin
d E
F.
Cal
cula
te E
Fby
add
ing
ED
and
DF
.
ED
#D
F$
EF
1.2
#1.
9 $
EF
3.1
$E
F
The
refo
re,E !
F!is
3.1
cen
tim
eter
s lo
ng.
E1.
2 cm
1.9
cm
FD
Fin
d x
and
AC
.
Bis
bet
wee
n A
and
C.
AB
#B
C$
AC
x#
2x$
2x#
53x
$2x
#5
x$
5A
C$
2x#
5 $
2(5)
#5
$15
Ax
2xC
B
2x "
5
Exam
ple1
Exam
ple1
Exam
ple2
Exam
ple2
Exercis
esExercis
es
Fin
d t
he
mea
sure
men
t of
eac
h s
egm
ent.
Ass
um
e th
at t
he
art
is n
ot d
raw
n t
o sc
ale.
1.R!
T!4.
5 cm
2.B!
C!3
!1 4!in
.
3.X!
Z!4!
1 4!in
.4.
W!X!
3 cm
Fin
d x
and
RS
if S
is b
etw
een
Ran
d T
.
5.R
S$
5x,S
T$
3x,a
nd R
T$
48.
6,30
6.R
S$
2x,S
T$
5x#
4,an
d R
T$
32.
4,8
7.R
S$
6x,S
T$
12,a
nd R
T$
72.
10,6
08.
RS
$4x
,R!S!
"S!T!
,and
RT
$24
.3,
12
Use
th
e fi
gure
s to
det
erm
ine
wh
eth
er e
ach
pai
r of
seg
men
ts i
s co
ngr
uen
t.
9.A !
B!an
d C!
D!ye
s10
.X!Y!
and
Y!Z!
noX
YZ
3x "
55x
# 1
9x 2
AD
CB
11 c
m
11 c
m
5 cm
5 cm
WY
6 cm X
XZ
Y
3 – 4 in.
31 – 2 in.
AC
6 in
.
23 – 4 in.
BR
T2.
0 cm
2.5
cm
S
Answers (Lesson 1-2)
© Glencoe/McGraw-Hill A6 Glencoe Geometry
Skil
ls P
ract
ice
Line
ar M
easu
re a
nd P
reci
sion
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
PE
RIO
D__
___
1-2
1-2
©G
lenc
oe/M
cGra
w-H
ill9
Gle
ncoe
Geo
met
ry
Lesson 1-2
Fin
d t
he
len
gth
of
each
lin
e se
gmen
t or
obj
ect.
1.2.
abou
t 55
mm
abou
t 2!
1 4!in
.
Fin
d t
he
pre
cisi
on f
or e
ach
mea
sure
men
t.
3.40
fee
t4.
12 c
enti
met
ers
5.9"
1 2"in
ches
0.5
ft0.
5 cm
!1 4!in
.
Fin
d t
he
mea
sure
men
t of
eac
h s
egm
ent.
6.N!
Q!7.
A!C!
8.G!
H!
2!1 4!
in.
10.1
cm
5.3
mm
Fin
d t
he
valu
e of
th
e va
riab
le a
nd
YZ
if Y
is b
etw
een
Xan
d Z
.
9.X
Y$
5p,Y
Z$
p,an
d X
Y$
2510
.XY
$12
,YZ
$2g
,and
XZ
$28
5;5
8;16
11.X
Y$
4m,Y
Z$
3m,a
nd X
Z$
4212
.XY
$2c
#1,
YZ
$6c
,and
XZ
$81
6;18
10;6
0
Use
th
e fi
gure
s to
det
erm
ine
wh
eth
er e
ach
pai
r of
seg
men
ts i
s co
ngr
uen
t.
13.B!
E!,C!
D!14
.M!P!,
N!P!
15.W!
X!,W!
Z!
yes
nono
YZ
WX
9 ft
5 ft
5 ft
NP
M10
yd
12 y
d
12 y
dE
D
CB
5 m
2 m
3 m
3 m
F9.
7 m
mH
G
15 m
mA
4.9
cm5.
2 cm
CB
Q1i
n.11 – 4 in
.
NP
12
in.
1cm
23
54
©G
lenc
oe/M
cGra
w-H
ill10
Gle
ncoe
Geo
met
ry
Fin
d t
he
len
gth
of
each
lin
e se
gmen
t or
obj
ect.
1.2.
1!1 11 6!
in.
42 m
m
Fin
d t
he
pre
cisi
on f
or e
ach
mea
sure
men
t.
3.12
0 m
eter
s4.
7"1 4"
inch
es5.
30.0
mill
imet
ers
0.5
m!1 8!
in.
0.5
mm
Fin
d t
he
mea
sure
men
t of
eac
h s
egm
ent.
6.P!S!
7.A!
D!8.
W!X!
23.1
cm
3!5 8!
in.
10.4
cm
Fin
d t
he
valu
e of
th
e va
riab
le a
nd
KL
if K
is b
etw
een
Jan
d L
.
9.JK
$6r
,KL
$3r
,and
JL
$27
10.J
K$
2s,K
L$
s#
2,an
d JL
$5s
!10
3;9
6;8
Use
th
e fi
gure
s to
det
erm
ine
wh
eth
er e
ach
pai
r of
seg
men
ts i
s co
ngr
uen
t.
11.T!
U!,S!
W!12
.A!D!
,B!C!
13.G!
F!,F!E!
noye
sno
14.C
AR
PEN
TRY
Jorg
e us
ed t
he f
igur
e at
the
rig
ht t
o m
ake
a pa
tter
n fo
r a
mos
aic
he p
lans
to
inla
y on
a t
able
top.
Nam
e al
l of
the
cong
ruen
t se
gmen
ts in
the
fig
ure.
B!C!
"F!E!
,A!B!
"C!
D!"
D!E!
"F!A!
DA
BF E
C
GH
EF5x
6xD
C
BA
12.9
in.
12.7
in.
W
TS
U
2 ft
2 ft
3 ft
3 ft
W89
.6 c
mY
X
100
cmA
11 – 4 in.
23 – 8 in.
DC
P4.
7 cm
18.4
cm
SQ
1cm
23
54
12
in.
EF
Pra
ctic
e (A
vera
ge)
Line
ar M
easu
re a
nd P
reci
sion
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
PE
RIO
D__
___
1-2
1-2
Answers (Lesson 1-2)
© Glencoe/McGraw-Hill A7 Glencoe Geometry
An
swer
s
Rea
din
g t
o L
earn
Math
emati
csLi
near
Mea
sure
and
Pre
cisi
on
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
PE
RIO
D__
___
1-2
1-2
©G
lenc
oe/M
cGra
w-H
ill11
Gle
ncoe
Geo
met
ry
Lesson 1-2
Pre-
Act
ivit
yW
hy
are
un
its
of m
easu
re i
mp
orta
nt?
Rea
d th
e in
trod
ucti
on t
o L
esso
n 1-
2 at
the
top
of
page
13
in y
our
text
book
.
•T
he b
asic
uni
t of
leng
th in
the
met
ric
syst
em is
the
met
er.H
ow m
any
met
ers
are
ther
e in
one
kilo
met
er?
1000
•D
o yo
u th
ink
it w
ould
be
easi
er t
o le
arn
the
rela
tion
ship
s be
twee
n th
edi
ffer
ent
unit
s of
leng
th in
the
cus
tom
ary
syst
em (
used
in t
he U
nite
dSt
ates
) or
in t
he m
etri
c sy
stem
? E
xpla
in y
our
answ
er.
Sam
ple
answ
er:
The
met
ric
syst
em is
eas
ier
beca
use
you
can
chan
gebe
twee
n th
e di
ffer
ent
units
by
just
mov
ing
the
deci
mal
poi
nt.
Rea
din
g t
he
Less
on
1.E
xpla
in t
he d
iffe
renc
e be
twee
n a
line
and
a li
ne s
egm
ent
and
why
one
of
thes
e ca
n be
mea
sure
d,w
hile
the
oth
er c
anno
t.S
ampl
e an
swer
:A li
ne is
infin
ite.S
ince
it h
as n
o en
dpoi
nts,
a lin
e do
esno
t ha
ve a
def
inite
leng
th a
nd c
anno
t be
mea
sure
d.A
line
seg
men
t ha
stw
o en
dpoi
nts,
so it
has
a d
efin
ite le
ngth
and
can
be
mea
sure
d.
2.W
hat
is t
he s
mal
lest
leng
th m
arke
d on
a 1
2-in
ch r
uler
?S
ampl
e an
swer
:!11 6!
in.
Wha
t is
the
sm
alle
st le
ngth
mar
ked
on a
cen
tim
eter
rul
er?
1 m
m
3.F
ind
the
prec
isio
n of
eac
h m
easu
rem
ent.
a.15
cm
0.5
cmb.
15.0
cm
0.05
cm
4.R
efer
to
the
figu
re a
t th
e ri
ght.
Whi
ch o
ne o
f th
e fo
llow
ing
stat
emen
ts is
tru
e? E
xpla
in y
our
answ
er.
A !B!
$C!
D!A!
B!"
C !D!
A!B!
"C!
D!;S
ampl
e an
swer
:The
tw
o se
gmen
ts a
re
cong
ruen
t be
caus
e th
ey h
ave
the
sam
e m
easu
re o
rle
ngth
.The
y ar
e no
t eq
ual b
ecau
se t
hey
are
not
the
sam
e se
gmen
t.
5.Su
ppos
e th
at S
is a
poi
nt o
n V!
W!an
d S
is n
ot t
he s
ame
poin
t as
Vor
W.T
ell w
heth
erea
ch o
f th
e fo
llow
ing
stat
emen
ts is
alw
ays,
som
etim
es,o
r ne
ver
true
.a.
VS
$S
Wso
met
imes
b.S
is b
etw
een
Van
d W
.al
way
sc.
VS
#V
W$
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neve
r
Hel
pin
g Y
ou
Rem
emb
er
6.A
goo
d w
ay t
o re
mem
ber
term
s us
ed in
mat
hem
atic
s is
to
rela
te t
hem
to
ever
yday
wor
dsyo
u kn
ow.G
ive
thre
e w
ords
tha
t ar
e us
ed o
utsi
de o
f m
athe
mat
ics
that
can
hel
p yo
ure
mem
ber
that
the
re a
re 1
00 c
enti
met
ers
in a
met
er.
Sam
ple
answ
er:c
ent,
cent
ury,
cent
enni
al
A
B
4.5
cm4.
5 cm
DC
©G
lenc
oe/M
cGra
w-H
ill12
Gle
ncoe
Geo
met
ry
Poin
ts E
quid
ista
nt fr
om S
egm
ents
The
dis
tanc
e fr
om a
poi
nt t
o a
segm
ent
is z
ero
if t
he p
oint
is o
n th
e se
gmen
t.O
ther
wis
e,it
is t
he le
ngth
of
the
shor
test
seg
men
t fr
om t
he
poin
t to
the
seg
men
t.
A f
igur
e is
a l
ocu
sif
it is
the
set
of
all p
oint
s th
at s
atis
fy
a se
t of
con
diti
ons.
The
locu
s of
all
poin
ts t
hat
are
"1 4"in
ch
from
the
seg
men
t A
Bis
sho
wn
by t
wo
dash
ed s
egm
ents
w
ith
sem
icir
cles
at
both
end
s.
1.Su
ppos
e A
,B,C
,and
Dar
e fo
ur d
iffe
rent
poi
nts,
and
cons
ider
the
locu
s of
all
poin
ts x
unit
s fr
om A!
B!an
dx
unit
s fr
om C!
D!.U
se a
ny u
nit
you
find
conv
enie
nt.T
he lo
cus
can
take
dif
fere
nt f
orm
s.Sk
etch
at
leas
t th
ree
poss
ibili
ties
.Lis
t so
me
of t
he t
hing
s th
at s
eem
to
affe
ct t
he f
orm
of
the
locu
s.S
ampl
e an
swer
s ar
e sh
own.
The
locu
s is
1Th
e lo
cus
is a
set
of
The
locu
s is
a p
air
segm
ent
X!Y! m
idw
ay2
poin
ts,X
and
Y.
of li
ne s
egm
ents
,be
twee
n A!
B!an
d C!
D!.
R!S!
and
P!Q!.
The
locu
s of
poi
nts
xun
its f
rom
A!B!
and
C!D!
depe
nds
on t
he
dist
ance
xan
d ho
w A!
B!an
d C!
D!ar
e si
tuat
ed r
elat
ive
to o
ne a
noth
er.
2.C
ondu
ct y
our
own
inve
stig
atio
n of
the
locu
s of
poi
nts
equi
dist
ant
from
tw
o se
gmen
ts.D
escr
ibe
your
res
ults
on
ase
para
te s
heet
of
pape
r.S
ee s
tude
nts’
wor
k.
AB
CD
PQ
RS
A
B
C
D
X
Y
AB
CD
XY
AB
En
rich
men
t
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
PE
RIO
D__
___
1-2
1-2
Answers (Lesson 1-2)
© Glencoe/McGraw-Hill A8 Glencoe Geometry
Stu
dy
Gu
ide
and I
nte
rven
tion
Dis
tanc
e an
d M
idpo
ints
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
PE
RIO
D__
___
1-3
1-3
©G
lenc
oe/M
cGra
w-H
ill13
Gle
ncoe
Geo
met
ry
Lesson 1-3
Dis
tan
ce B
etw
een
Tw
o P
oin
ts
Dis
tanc
e on
a N
umbe
r Li
neD
ista
nce
in t
he C
oord
inat
e P
lane
AB
$|b
!a
|or
|a!
b|
x
y
OC
( 1, –
1)A
( –2,
–1)
B( 1
, 3)
Pyt
hago
rean
The
orem
:
a2#
b2$
c2
Dis
tanc
e F
orm
ula:
d$
#(x
2!
!x 1
)2#
!(y
2!
!y 1
)2!
AB
ab
Fin
d A
B.
AB
$|(!
4) !
2|$
|!6|
$6
#5
#4
#3
#2
#1
01
23
AB
Fin
d t
he
dis
tan
ce b
etw
een
A
(!2,
!1)
an
d B
(1,3
).
Exam
ple1
Exam
ple1
Exam
ple2
Exam
ple2
Pyt
hag
orea
n T
heo
rem
(AB
)2$
(AC
)2#
(BC
)2
(AB
)2$
(3)2
#(4
)2
(AB
)2$
25
AB
$#
25!$
5
Dis
tan
ce F
orm
ula
d$
#(x
2!
!x 1
)2#
!(y
2!
!y 1
)2!
AB
$#
(1 !
(!
!2)
)2!
#(3
!!
(!1)
)!
2 !A
B$
#(3
)2#
!(4
)2!
$#
25!$
5
Use
th
e n
um
ber
lin
e to
fin
d e
ach
mea
sure
.
1.B
D6
2.D
G9
3.A
F12
4.E
F3
5.B
G15
6.A
G17
7.B
E7
8.D
E1
Use
th
e P
yth
agor
ean
Th
eore
m t
o fi
nd
th
e d
ista
nce
bet
wee
n e
ach
pai
r of
poi
nts
.
9.A
(0,0
),B
(6,8
)10
10.R
(!2,
3),S
(3,1
5)13
11.M
(1,!
2),N
(9,1
3)17
12.E
(!12
,2),
F(!
9,6)
5
Use
th
e D
ista
nce
For
mu
la t
o fi
nd
th
e d
ista
nce
bet
wee
n e
ach
pai
r of
poi
nts
.
13.A
(0,0
),B
(15,
20)
2514
.O(!
12,0
),P
(!8,
3)5
15.C
(11,
!12
),D
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221
!$
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16.E
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10),
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4,3)
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$7.
3
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–8–6
–4–2
02
46
8
AB
CD
EF
G
Exercis
esExercis
es
©G
lenc
oe/M
cGra
w-H
ill14
Gle
ncoe
Geo
met
ry
Mid
po
int
of
a Se
gm
ent
Mid
poin
t on
aIf
the
coor
dina
tes
of th
e en
dpoi
nts
of a
seg
men
t are
aan
d b,
Num
ber
Line
then
the
coor
dina
te o
f the
mid
poin
t of t
he s
egm
ent i
s "a
# 2b
".
Mid
poin
t on
aIf
a se
gmen
t has
end
poin
ts w
ith c
oord
inat
es (
x 1, y
1) a
nd (
x 2, y
2),
Coo
rdin
ate
Pla
neth
en th
e co
ordi
nate
s of
the
mid
poin
t of t
he s
egm
ent a
re $"x 1
# 2x 2
", "
y 1# 2
y 2"
%.
Fin
d t
he
coor
din
ate
of t
he
mid
poi
nt
of P!
Q!.
The
coo
rdin
ates
of P
and
Qar
e !
3 an
d 1.
If M
is t
he m
idpo
int
of P!
Q!,t
hen
the
coor
dina
te o
f Mis
"!3 2#
1"
$"! 22 "
or !
1.
Mis
th
e m
idp
oin
t of
P !Q!
for
P(#
2,4)
an
d Q
(4,1
).F
ind
th
eco
ord
inat
es o
f M
.
M$
$"x 1# 2
x 2"
,"y 1
# 2y 2
"%$
$"!2 2#
4"
,"4
# 21
"%o
r (1
,2.5
)
Use
th
e n
um
ber
lin
e to
fin
d t
he
coor
din
ate
of
the
mid
poi
nt
of e
ach
seg
men
t.
1.C !
E!#
12.
D!G!
4
3.A!
F!#
34.
E!G!
5
5.A!
B!#
86.
B!G!
!1 2!
7.B!
D!#
3!1 2!
8.D!
E!1
Fin
d t
he
coor
din
ates
of
the
mid
poi
nt
of a
seg
men
t h
avin
g th
e gi
ven
en
dp
oin
ts.
9.A
(0,0
),B
(12,
8)(6
,4)
10.R
(!12
,8),
S(6
,12)
(#3,
10)
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(11,
!2)
,N(!
9,13
)(1
,5.5
)12
.E(!
2,6)
,F(!
9,3)
(#5.
5,4.
5)
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(10,
!22
),T
(9,1
0)(9
.5,#
6)14
.M(!
11,2
),N
(!19
,6)
(#15
,4)
–10
–8–6
–4–2
02
46
8
AB
CD
EF
G
–3–2
–10
12
PQ
Stu
dy
Gu
ide
and I
nte
rven
tion
(con
tinu
ed)
Dis
tanc
e an
d M
idpo
ints
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
PE
RIO
D__
___
1-3
1-3
Exam
ple1
Exam
ple1
Exam
ple2
Exam
ple2
Exercis
esExercis
es
Answers (Lesson 1-3)
© Glencoe/McGraw-Hill A9 Glencoe Geometry
An
swer
s
Skil
ls P
ract
ice
Dis
tanc
e an
d M
idpo
ints
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
PE
RIO
D__
___
1-3
1-3
©G
lenc
oe/M
cGra
w-H
ill15
Gle
ncoe
Geo
met
ry
Lesson 1-3
Use
th
e n
um
ber
lin
e to
fin
d e
ach
mea
sure
.
1.L
N6
2.JL
8
3.K
N11
4.M
N3
Use
th
e P
yth
agor
ean
Th
eore
m t
o fi
nd
th
e d
ista
nce
bet
wee
n e
ach
pai
r of
poi
nts
.
5.5
6.10
7.K
(2,3
),F
(4,4
)8.
C(!
3,!
1),Q
(!2,
3)
#5!
$2.
2#
17!$
4.1
Use
th
e D
ista
nce
For
mu
la t
o fi
nd
th
e d
ista
nce
bet
wee
n e
ach
pai
r of
poi
nts
.
9.Y
(2,0
),P
(2,6
)10
.W(!
2,2)
,R(5
,2)
67
11.A
(!7,
!3)
,B(5
,2)
12.C
(!3,
1),Q
(2,6
)
13#
50!$
7.1
Use
th
e n
um
ber
lin
e to
fin
d t
he
coor
din
ate
of t
he
mid
poi
nt
of e
ach
seg
men
t.
13.D !
E!9
14.B!
C!1
15.B!
D!3
16.A!
D!1!
1 2!
Fin
d t
he
coor
din
ates
of
the
mid
poi
nt
of a
seg
men
t h
avin
g th
e gi
ven
en
dp
oin
ts.
17.T
(3,1
),U
(5,3
)18
.J(!
4,2)
,F(5
,!2)
(4,2
)%!1 2! ,
0 &F
ind
th
e co
ord
inat
es o
f th
e m
issi
ng
end
poi
nt
give
n t
hat
Pis
th
e m
idp
oin
t of
N!Q!
.
19.N
(2,0
),P
(5,2
)20
.N(5
,4),
P(6
,3)
21.Q
(3,9
),P
(!1,
5)
Q(8
,4)
Q(7
,2)
N(#
5,1)
–6–4
–20
24
68
1012
AB
CD
E
x
y
O
D
S
x
y
O
F
G
–6–4
–20
24
68
10
JK
LM
N
©G
lenc
oe/M
cGra
w-H
ill16
Gle
ncoe
Geo
met
ry
Use
th
e n
um
ber
lin
e to
fin
d e
ach
mea
sure
.
1.V
W4
2.T
V5
3.S
T3
4.S
V8
Use
th
e P
yth
agor
ean
Th
eore
m t
o fi
nd
th
e d
ista
nce
bet
wee
n e
ach
pai
r of
poi
nts
.
5.6.
#65!
$8.
1#
113
!$
10.6
Use
th
e D
ista
nce
For
mu
la t
o fi
nd
th
e d
ista
nce
bet
wee
n e
ach
pai
r of
poi
nts
.
7.L
(!7,
0),Y
(5,9
)8.
U(1
,3),
B(4
,6)
15#
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4.2
Use
th
e n
um
ber
lin
e to
fin
d t
he
coor
din
ate
of t
he
mid
poi
nt
of e
ach
seg
men
t.
9.R !
T!1
10.Q!
R!#
4
11.S!
T!2!
1 2!12
.P!R!
#5
!1 2!
Fin
d t
he
coor
din
ates
of
the
mid
poi
nt
of a
seg
men
t h
avin
g th
e gi
ven
en
dp
oin
ts.
13.K
(!9,
3),H
(5,7
)14
.W(!
12,!
7),T
(!8,
!4)
(#2,
5)(#
10,#
5.5)
Fin
d t
he
coor
din
ates
of
the
mis
sin
g en
dp
oin
t gi
ven
th
at E
is t
he
mid
poi
nt
of D!
F!.
15.F
(5,8
),E
(4,3
)16
.F(2
,9),
E(!
1,6)
17.D
(!3,
!8)
,E(1
,!2)
D(3
,#2)
D(#
4,3)
F(5
,4)
18.P
ERIM
ETER
The
coo
rdin
ates
of
the
vert
ices
of
a qu
adri
late
ral a
re R
(!1,
3),S
(3,3
),T
(5,!
1),a
nd U
(!2,
!1)
.Fin
d th
e pe
rim
eter
of
the
quad
rila
tera
l.R
ound
to
the
near
est
tent
h.19
.6 u
nits
–6–4
–10
–8–2
02
46
PQ
RS
T
x
y
O
E
S
x
y
OM
Z
–6–4
–10
–8–2
02
46
8
ST
UV
W
Pra
ctic
e (A
vera
ge)
Dis
tanc
e an
d M
idpo
ints
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
PE
RIO
D__
___
1-3
1-3
Answers (Lesson 1-3)
© Glencoe/McGraw-Hill A10 Glencoe Geometry
Rea
din
g t
o L
earn
Math
emati
csD
ista
nce
and
Mid
poin
ts
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
PE
RIO
D__
___
1-3
1-3
©G
lenc
oe/M
cGra
w-H
ill17
Gle
ncoe
Geo
met
ry
Lesson 1-3
Pre-
Act
ivit
yH
ow c
an y
ou f
ind
th
e d
ista
nce
bet
wee
n t
wo
poi
nts
wit
hou
t a
rule
r?
Rea
d th
e in
trod
ucti
on t
o L
esso
n 1-
3 at
the
top
of
page
21
in y
our
text
book
.
•L
ook
at t
he t
rian
gle
in t
he in
trod
ucti
on t
o th
is le
sson
.Wha
t is
the
spe
cial
nam
e fo
r A!
B!in
thi
s tr
iang
le?
hypo
tenu
se•
Fin
d A
Bin
thi
s fi
gure
.Wri
te y
our
answ
er b
oth
as a
rad
ical
and
as
ade
cim
al n
umbe
r ro
unde
d to
the
nea
rest
ten
th.
#61!
units
;7.8
uni
ts
Rea
din
g t
he
Less
on
1.M
atch
eac
h fo
rmul
a or
exp
ress
ion
in t
he f
irst
col
umn
wit
h on
e of
the
nam
es in
the
seco
nd c
olum
n.
a.d
$#
(x2
!!
x 1)2
#!
(y2
!!
y 1)2
!ii
i.P
ytha
gore
an T
heor
em
b."a
# 2b
"v
ii.D
ista
nce
Form
ula
in t
he C
oord
inat
e P
lane
c.X
Y$
| a!
b|iv
iii.
Mid
poin
t of
a S
egm
ent
in t
he C
oord
inat
e P
lane
d.c2
$a2
#b2
iiv
.D
ista
nce
Form
ula
on a
Num
ber
Lin
e
e.$"x 1
# 2x 2
","
y 1# 2
y 2"
%iii
v.M
idpo
int
of a
Seg
men
t on
a N
umbe
r L
ine
2.F
ill in
the
ste
ps t
o ca
lcul
ate
the
dist
ance
bet
wee
n th
e po
ints
M(4
,!3)
and
N(!
2,7)
.
Let
(x 1
,y1)
$(4
,!3)
.The
n (x
2,y 2
) $(
,).
d$
#!
!!
!(
!)2
#(
!)2
MN
$#!
!!
!(
!)2
#(
!)2
MN
$#!
!(
)2#
()2
MN
$#!
!#
MN
$#!
Fin
d a
deci
mal
app
roxi
mat
ion
for
MN
to t
he n
eare
st h
undr
edth
.11
.66
Hel
pin
g Y
ou
Rem
emb
er
3.A
goo
d w
ay t
o re
mem
ber
a ne
w f
orm
ula
in m
athe
mat
ics
is t
o re
late
it t
o on
e yo
u al
read
ykn
ow.I
f yo
u fo
rget
the
Dis
tanc
e Fo
rmul
a,ho
w c
an y
ou u
se t
he P
ytha
gore
an T
heor
em t
ofi
nd t
he d
ista
nce
dbe
twee
n tw
o po
ints
on
a co
ordi
nate
pla
ne?
Sam
ple
answ
er:I
f th
ese
gmen
t de
term
ined
by
the
poin
ts is
nei
ther
hor
izon
tal n
or v
ertic
al,d
raw
a ri
ght
tria
ngle
tha
t ha
s th
e se
gmen
t as
its
hypo
tenu
se.T
he h
oriz
onta
l si
de w
ill h
ave
leng
th |x
2#
x 1|a
nd t
he v
ertic
al s
ide
will
hav
e le
ngth
|y 2
#y 1
|.By
the
Pyt
hago
rean
The
orem
,d2
$|x 2
#x 1
|2"
|y 2#
y 1|2
$
(x 2#
x 1)2
"(y 2
#y 1
)2 .
136
100
36
10#
6
#3
74
#2
y 1y 2
x 1x 2
7#
2
©G
lenc
oe/M
cGra
w-H
ill18
Gle
ncoe
Geo
met
ry
Leng
ths
on a
Gri
dE
venl
y-sp
aced
hor
izon
tal a
nd v
erti
cal l
ines
for
m a
gri
d.
You
can
easi
ly f
ind
segm
ent
leng
ths
on
a gr
id if
the
end
poin
ts a
re g
rid-
line
inte
rsec
tion
s.Fo
r ho
rizo
ntal
or
vert
ical
segm
ents
,sim
ply
coun
t sq
uare
s.Fo
r di
agon
al s
egm
ents
,use
the
Pyt
hago
rean
The
orem
(pr
oven
in C
hapt
er 7
).T
his
theo
rem
sta
tes
that
in a
ny r
ight
tri
angl
e,if
the
leng
th o
f th
e lo
nges
t si
de (
the
side
oppo
site
the
rig
ht a
ngle
) is
can
d th
e tw
osh
orte
r si
des
have
leng
ths
aan
d b,
then
c2
$a2
#b2
.
Fin
d t
he
mea
sure
of
E !F!
on t
he
grid
at
the
righ
t.L
ocat
e a
righ
t tr
ian
gle
wit
h E !
F!as
its
lo
nge
st s
ide.
EF
$#
22#
5!
2 !$#
29!&
5.4
unit
s
Fin
d e
ach
mea
sure
to
the
nea
rest
ten
th o
f a
un
it.
1.I!J!
32.
M!N!
73.
R!S!
4.2
4.Q!
S!5.
8
5.I!K!
7.6
6.J!K!
57.
L!M!
4.1
8.L!N!
7.2
Use
th
e gr
id a
bove
.Fin
d t
he
per
imet
er o
f ea
ch t
rian
gle
to t
he
nea
rest
ten
th
of a
un
it.
9.!
AB
C20
.210
.!
QR
S18
11.
!D
EF
16.6
12.
!L
MN
18.3
Ans
wer
s sh
own
are
foun
d by
rou
ndin
g se
gmen
t le
ngth
s be
fore
add
ing.
13.O
f al
l the
seg
men
ts s
how
n on
the
14.O
n th
e gr
id,1
uni
t$0.
5 cm
.How
can
the
gr
id,w
hich
is lo
nges
t? W
hat
is it
san
swer
s ab
ove
be u
sed
to f
ind
the
mea
sure
s le
ngth
?B
C!
8.1
in c
enti
met
ers?
D
ivid
e by
2 o
r m
ultip
ly b
y 0.
5.
15.U
se y
our
answ
er f
rom
exe
rcis
e 8
to16
.Use
a c
enti
met
er r
uler
to
find
the
per
imet
er
calc
ulat
e th
e le
ngth
of
segm
ent
LN
of t
rian
gle
IJK
to t
he n
eare
st t
enth
of
a
in c
enti
met
ers.
Che
ck b
y m
easu
ring
cent
imet
er.
7.8
cmw
ith
a ce
ntim
eter
rul
er.
3.6
cm
E 2
5F
A B F
I J
KN
M
C
D
E
S
R Q L
En
rich
men
t
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
PE
RIO
D__
___
1-3
1-3
Exam
ple
Exam
ple
Answers (Lesson 1-3)
© Glencoe/McGraw-Hill A11 Glencoe Geometry
An
swer
s
Stu
dy
Gu
ide
and I
nte
rven
tion
Ang
le M
easu
re
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
PE
RIO
D__
___
1-4
1-4
©G
lenc
oe/M
cGra
w-H
ill19
Gle
ncoe
Geo
met
ry
Lesson 1-4
Mea
sure
An
gle
sIf
tw
o no
ncol
linea
r ra
ysha
ve a
com
mon
en
dpoi
nt,t
hey
form
an
angl
e.T
he r
ays
are
the
sid
esof
the
ang
le.
The
com
mon
end
poin
t is
the
ver
tex.
The
ang
le a
t th
e ri
ght
can
be
nam
ed a
s "
A,"
BA
C,"
CA
B,o
r "
1.
A r
igh
t an
gle
is a
n an
gle
who
se m
easu
re is
90.
An
acu
te a
ngl
eha
s m
easu
re le
ss t
han
90.A
n ob
tuse
an
gle
has
mea
sure
gre
ater
th
an 9
0 bu
t le
ss t
han
180.
AC
B
1
a.N
ame
all
angl
es t
hat
hav
e R
as a
vert
ex.
Thr
ee a
ngle
s ar
e "
1,"
2,an
d "
3.Fo
rot
her
angl
es,u
se t
hree
lett
ers
to n
ame
them
:"S
RQ
,"P
RT
,and
"S
RT
.
b.N
ame
the
sid
es o
f !
1.
RS
" "# ,
RP
""#
SR
T
PQ
12
3
Mea
sure
eac
h a
ngl
e an
dcl
assi
fy i
t as
rig
ht,
acu
te,o
r ob
tuse
.
a.!
AB
DU
sing
a p
rotr
acto
r,m
"A
BD
$50
.50
%90
,so
"A
BD
is a
n ac
ute
angl
e.
b.!
DB
CU
sing
a p
rotr
acto
r,m
"D
BC
$11
5.18
0 &
115
&90
,so
"D
BC
is a
n ob
tuse
angl
e.
c.!
EB
CU
sing
a p
rotr
acto
r,m
"E
BC
$90
."
EB
Cis
a r
ight
ang
le.
BA
DE
C
Exam
ple1
Exam
ple1
Exam
ple2
Exam
ple2
Exercis
esExercis
es
Ref
er t
o th
e fi
gure
.
1.N
ame
the
vert
ex o
f "4.
B
2.N
ame
the
side
s of
"B
DC
.D
B""
# ,D
C""#
3.W
rite
ano
ther
nam
e fo
r "
DB
C.
!3
or !
CB
D
Mea
sure
eac
h a
ngl
e in
th
e fi
gure
an
d c
lass
ify
it a
s ri
ght,
acu
te,o
r ob
tuse
.
4."
MP
R12
0;ob
tuse
5."
RP
N90
;rig
ht
6."
NP
S45
;acu
te
P
NM
R
S
C
BA
12
34
D
©G
lenc
oe/M
cGra
w-H
ill20
Gle
ncoe
Geo
met
ry
Co
ng
ruen
t A
ng
les
Ang
les
that
hav
e th
e sa
me
mea
sure
are
co
ngr
uen
t an
gles
.A r
ay t
hat
divi
des
an a
ngle
into
tw
o co
ngru
ent
angl
es is
cal
led
an a
ngl
e bi
sect
or.I
n th
e fi
gure
,PN
" "#
is t
he a
ngle
bi
sect
or o
f "M
PR
.Poi
nt N
lies
in t
he in
teri
or o
f "M
PR
and
"M
PN
""
NP
R. R
efer
to
the
figu
re a
bove
.If
m!
MP
N$
2x"
14 a
nd
m
!N
PR
$x
"34
,fin
d x
and
fin
d m
!M
PR
.Si
nce
PN
" "#
bise
cts
"M
PR
,"M
PN
""
NP
R,o
r m
"M
PN
$m
"N
PR
.
2x#
14 $
x#
34m
"N
PR
$(2
x#
14)
#(x
#34
)2x
#14
!x
$x
#34
!x
$54
#54
x#
14 $
34$
108
x#
14 !
14 $
34 !
14x
$20
QS
" "#
bise
cts
!P
QT
,an
d Q
P""
#an
d Q
R""
#ar
e op
pos
ite
rays
.
1.If
m"
PQ
T$
60 a
nd m
"P
QS
$4x
#14
,fin
d th
e va
lue
of x
.
4
2.If
m"
PQ
S$
3x#
13 a
nd m
"S
QT
$6x
!2,
find
m"
PQ
T.
56
BA
""#
and
BC
""#
are
opp
osit
e ra
ys,B
F""
#bi
sect
s !
CB
E,a
nd
B
D" "
#bi
sect
s !
AB
E.
3.If
m"
EB
F$
6x#
4 an
d m
"C
BF
$7x
!2,
find
m"
EB
C.
80
4.If
m"
1 $
4x#
10 a
nd m
"2
$5x
,fin
d m
"2.
50
5.If
m"
2 $
6y#
2 an
d m
"1
$8y
!14
,fin
d m
"A
BE
.
100
6.Is
"D
BF
a ri
ght
angl
e? E
xpla
in.
Yes;
sinc
e B
D""
#an
d B
F""
# are
bis
ecto
rs,m
!2
"m
!3
mus
t eq
ual h
alf
the
tota
l ang
le m
easu
re,a
nd h
alf
of 1
80 is
90.
BA
CF
ED
12
34
QP
R
TS
PR
NM
Stu
dy
Gu
ide
and I
nte
rven
tion
(con
tinu
ed)
Ang
le M
easu
re
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
PE
RIO
D__
___
1-4
1-4
Exam
ple
Exam
ple
Exercis
esExercis
es
Answers (Lesson 1-4)
© Glencoe/McGraw-Hill A12 Glencoe Geometry
Skil
ls P
ract
ice
Ang
le M
easu
re
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
PE
RIO
D__
___
1-4
1-4
©G
lenc
oe/M
cGra
w-H
ill21
Gle
ncoe
Geo
met
ry
Lesson 1-4
For
Exe
rcis
es 1
–12,
use
th
e fi
gure
at
the
righ
t.
Nam
e th
e ve
rtex
of
each
an
gle.
1."
4T
2."
1W
3."
2V
4."
5T
Nam
e th
e si
des
of
each
an
gle.
5."
46.
"5
TU""# ,
TS""#
TS""# ,
TW""#
7."
ST
V8.
"1
TS""# ,
TV""#
WT
""# ,
WV
""#
Wri
te a
not
her
nam
e fo
r ea
ch a
ngl
e.
9."
310
."4
!W
TV,!
VTW
!U
TS,!
STU
11."
WT
S12
."2
!S
TW,!
5!
WV
T,!
TVW
,!W
VU
,!U
VW
Mea
sure
eac
h a
ngl
e an
d c
lass
ify
it a
s ri
ght,
acu
te,
or o
btu
se.
13."
NM
P14
."O
MN
90%,
righ
t40
%,ac
ute
15."
QM
N16
."Q
MO
140%
,obt
use
100%
,obt
use
ALG
EBR
AIn
th
e fi
gure
,BA
""#
and
BC
""#
are
opp
osit
e ra
ys,
BD
" "#
bise
cts
!E
BC
,an
d B
F""
#bi
sect
s !
AB
E.
17.I
f m
"E
BD
$4x
#16
and
m"
DB
C$
6x#
4,fi
nd m
"E
BD
.40
18.I
f m
"A
BF
$7x
!8
and
m"
EB
F$
5x#
10,
find
m"
EB
F.
55
BC
A
FE
D
MN
L
QO
P
U T VW
S5
3 21
4
©G
lenc
oe/M
cGra
w-H
ill22
Gle
ncoe
Geo
met
ry
For
Exe
rcis
es 1
–10,
use
th
e fi
gure
at
the
righ
t.
Nam
e th
e ve
rtex
of
each
an
gle.
1."
5M
2."
3P
3."
8O
4."
NM
PM
Nam
e th
e si
des
of
each
an
gle.
5."
66.
"2
NM""
# ,N
O""
#or
NP
""#
or N
R""
#P
R""# ,
PM""
#
7."
MO
P8.
"O
MN
OM
""# ,
OP
""# o
r O
R""
#M
O""
# ,M
N""
#
Wri
te a
not
her
nam
e fo
r ea
ch a
ngl
e.
9."
QP
R10
."1
!3,
!R
PQ
!M
PO
,!O
PM
,!M
PN
,!N
PM
Mea
sure
eac
h a
ngl
e an
d c
lass
ify
it a
s ri
ght,
acu
te,
or o
btu
se.
11."
UZ
W12
."Y
ZW
90%,
righ
t70
%,ac
ute
13."
TZ
W14
."U
ZT
110%
,obt
use
20%,
acut
e
ALG
EBR
AIn
th
e fi
gure
,CB
""#
and
CD
""#
are
opp
osit
e ra
ys,
CE
" "#
bise
cts
!D
CF
,an
d C
G""
#bi
sect
s !
FC
B.
15.I
f m
"D
CE
$4x
#15
and
m"
EC
F$
6x!
5,fi
nd m
"D
CE
.55
16.I
f m
"F
CG
$9x
#3
and
m"
GC
B$
13x
!9,
find
m"
GC
B.
30
17.T
RA
FFIC
SIG
NS
The
dia
gram
sho
ws
a si
gn u
sed
to w
arn
driv
ers
of a
sch
ool z
one
or c
ross
ing.
Mea
sure
and
cla
ssif
y ea
ch n
umbe
red
angl
e.
m!
1 $
90,r
ight
ang
le;m
!2
$13
0,ob
tuse
2 1BC
G
F
EDZ
YTU
VW
X
N
O
PQ
R
M1 2
8
3
54
6
7
Pra
ctic
e (A
vera
ge)
Ang
le M
easu
re
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
PE
RIO
D__
___
1-4
1-4
Answers (Lesson 1-4)
© Glencoe/McGraw-Hill A13 Glencoe Geometry
An
swer
s
Rea
din
g t
o L
earn
Math
emati
csA
ngle
Mea
sure
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
PE
RIO
D__
___
1-4
1-4
©G
lenc
oe/M
cGra
w-H
ill23
Gle
ncoe
Geo
met
ry
Lesson 1-4
Pre-
Act
ivit
yH
ow b
ig i
s a
deg
ree?
Rea
d th
e in
trod
ucti
on t
o L
esso
n 1-
4 at
the
top
of
page
29
in y
our
text
book
.•
A s
emic
ircl
e is
hal
f a
circ
le.H
ow m
any
degr
ees
are
ther
e in
a
sem
icir
cle?
180
•H
ow m
any
degr
ees
are
ther
e in
a q
uart
er c
ircl
e?90
Rea
din
g t
he
Less
on
1.M
atch
eac
h de
scri
ptio
n in
the
fir
st c
olum
n w
ith
one
of t
he t
erm
s in
the
sec
ond
colu
mn.
Som
e te
rms
in t
he s
econ
d co
lum
n m
ay b
e us
ed m
ore
than
onc
e or
not
at
all.
a.a
figu
re m
ade
up o
f tw
o no
ncol
linea
r ra
ys w
ith
a1.
vert
ex
com
mon
end
poin
t4
2.an
gle
bise
ctor
b.an
gles
who
se d
egre
e m
easu
res
are
less
tha
n 90
83.
oppo
site
ray
sc.
angl
es t
hat
have
the
sam
e m
easu
re6
4.an
gle
d.an
gles
who
se d
egre
e m
easu
res
are
betw
een
90 a
nd 1
805
5.ob
tuse
ang
les
e.a
tool
use
d to
mea
sure
ang
les
106.
cong
ruen
t an
gles
f.th
e co
mm
on e
ndpo
int
of t
he r
ays
that
for
m a
n an
gle
17.
righ
t an
gles
g.a
ray
that
div
ides
an
angl
e in
to t
wo
cong
ruen
t an
gles
28.
acut
e an
gles
9.co
mpa
ss10
.pro
trac
tor
2.U
se t
he f
igur
e to
nam
e ea
ch o
f th
e fo
llow
ing.
a.a
righ
t an
gle
!A
BE
or !
EB
Gb.
an o
btus
e an
gle
!A
BF
or !
AB
Cc.
an a
cute
ang
le!
EB
F,!
FBC
,!C
BG
,!E
BC
,or
!FB
Gd.
a po
int
in t
he in
teri
or o
f "E
BC
Fe.
a po
int
in t
he e
xter
ior
of "
EB
AF,
C,o
r G
f.th
e an
gle
bise
ctor
of "
EB
CB
F""#
g.a
poin
t on
"C
BE
C,B
,or
Eh
.th
e si
des
of "
AB
FB
A""#
and
BF""#
i.a
pair
of
oppo
site
ray
sB
A""#
and
BG
""#
j.th
e co
mm
on v
erte
x of
all
angl
es s
how
n in
the
fig
ure
Bk.
a pa
ir o
f co
ngru
ent
angl
es!
EB
Fan
d !
FBC
,or
!A
BE
and
!E
BG
l.th
e an
gle
wit
h th
e gr
eate
st m
easu
re!
AB
G
Hel
pin
g Y
ou
Rem
emb
er3.
A g
ood
way
to
rem
embe
r re
late
d ge
omet
ric
idea
s is
to
com
pare
the
m a
nd s
ee h
ow t
hey
are
alik
e an
d ho
w t
hey
are
diff
eren
t.G
ive
som
e si
mila
riti
es a
nd d
iffe
renc
es b
etw
een
cong
ruen
t se
gmen
tsan
d co
ngru
ent
angl
es.
Sam
ple
answ
er:C
ongr
uent
seg
men
ts a
nd c
ongr
uent
ang
les
are
alik
ebe
caus
e th
ey b
oth
invo
lve
a pa
ir o
f fig
ures
with
the
sam
e m
easu
re.T
hey
are
diff
eren
t be
caus
e co
ngru
ent
segm
ents
hav
e th
e sa
me
leng
th,w
hich
can
be m
easu
red
in u
nits
suc
h as
inch
es o
r ce
ntim
eter
s,w
hile
con
grue
ntan
gles
hav
e th
e sa
me
degr
ee m
easu
re.
BG
28% 28
%
A
EF
CD
©G
lenc
oe/M
cGra
w-H
ill24
Gle
ncoe
Geo
met
ry
Ang
le R
elat
ions
hips
Ang
les
are
mea
sure
d in
deg
rees
(').
Eac
h de
gree
of
an a
ngle
is d
ivid
-ed
into
60
min
utes
((),
and
each
min
ute
of a
n an
gle
is
divi
ded
into
60
seco
nds
()).
60(
$1'
60)
$1(
67"1 2" '
$67
'30(
70.4
'$
70°2
4(90
'$
89°6
0(
Tw
o an
gles
are
com
ple
men
tary
if
the
sum
of
thei
r m
easu
res
is 9
0%.
Fin
d t
he
com
ple
men
t of
eac
h o
f th
e fo
llow
ing
angl
es.
1.35
'15(
2.27
'16(
3.15
'54(
54%4
5&62
%44&
74%0
6&
4.29
'18(
22)
5.34
'29(
45)
6.87
'2(3
)
60%4
1&38
'55
%30&
15'
2%57
&57'
Tw
o an
gles
are
su
pp
lem
enta
ry i
f th
e su
m o
f th
eir
mea
sure
s is
180
%.F
ind
th
e su
pp
lem
ent
of e
ach
of
the
foll
owin
g an
gles
.
7.12
0'18
(8.
84'1
2(9.
110'
2(
59%4
2&95
%48&
69%5
8&
10.4
5'16
(24)
11.3
9'21
(54)
12.1
29'1
8(36
)
134%
43&3
6'14
0%38
&6'
50%4
1&24
'
13.9
8'52
(59)
14.9
'2(3
2)15
.1'2
(3)
81%7
&1'
170%
57&2
8'17
8%57
&57'
En
rich
men
t
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
PE
RIO
D__
___
1-4
1-4
Answers (Lesson 1-4)
© Glencoe/McGraw-Hill A14 Glencoe Geometry
Stu
dy
Gu
ide
and I
nte
rven
tion
Ang
le R
elat
ions
hips
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
PE
RIO
D__
___
1-5
1-5
©G
lenc
oe/M
cGra
w-H
ill25
Gle
ncoe
Geo
met
ry
Lesson 1-5
Pair
s o
f A
ng
les
Ad
jace
nt
angl
esar
e an
gles
in t
he s
ame
plan
e th
at h
ave
a co
mm
onve
rtex
and
a c
omm
on s
ide,
but
no c
omm
on in
teri
or p
oint
s.V
erti
cal
angl
esar
e tw
ono
nadj
acen
t an
gles
for
med
by
two
inte
rsec
ting
line
s.A
pai
r of
adj
acen
t an
gles
who
seno
ncom
mon
sid
es a
re o
ppos
ite
rays
is c
alle
d a
lin
ear
pai
r.
Iden
tify
eac
h p
air
of a
ngl
es a
s a
dja
cen
t a
ngl
es,v
erti
cal
an
gles
,an
d/o
r as
a l
inea
r pa
ir.
Exam
ple
Exam
ple
a.
"S
RT
and
"T
RU
have
a c
omm
onve
rtex
and
a c
omm
on s
ide,
but
noco
mm
on in
teri
or p
oint
s.T
hey
are
adja
cent
ang
les.
c.
"6
and
"5
are
adja
cent
ang
les
who
seno
ncom
mon
sid
es a
re o
ppos
ite
rays
.T
he a
ngle
s fo
rm a
line
ar p
air.
D
CB
A
56
RUT
Sb.
"1
and
"3
are
nona
djac
ent
angl
es f
orm
edby
tw
o in
ters
ecti
ng li
nes.
The
y ar
e ve
rtic
alan
gles
."2
and
"4
are
also
ver
tica
l ang
les.
d.
"A
and
"B
are
two
angl
es w
hose
mea
sure
sha
ve a
sum
of
90.T
hey
are
com
plem
enta
ry.
"F
and
"G
are
two
angl
es w
hose
mea
sure
sha
ve a
sum
of
180.
The
y ar
e su
pple
men
tary
.
AB
FG
30%
60%
60%
120%
N
RP
SM
14
32
Exercis
esExercis
es
Iden
tify
eac
h p
air
of a
ngl
es a
s a
dja
cen
t,ve
rtic
al,
and
/or
as a
lin
ear
pair
.
1."
1 an
d "
22.
"1
and
"6
adja
cent
linea
r pa
ir;a
djac
ent
3."
1 an
d "
54.
"3
and
"2
vert
ical
adja
cent
For
Exe
rcis
es 5
–7,r
efer
to
the
figu
re a
t th
e ri
ght.
5.Id
enti
fy t
wo
obtu
se v
erti
cal a
ngle
s.!
RN
Tan
d !
SN
U
6.Id
enti
fy t
wo
acut
e ad
jace
nt a
ngle
s.!
RN
V a
nd!
VN
Tor
!
VN
Tan
d !
TNU
7.Id
enti
fy a
n an
gle
supp
lem
enta
ry t
o "
TN
U.
!U
NS
or !
TNR
8.F
ind
the
mea
sure
s of
tw
o co
mpl
emen
tary
ang
les
if th
e di
ffer
ence
in t
heir
mea
sure
s is
18.
36 a
nd 5
4
RS
NU
TV
RS
TU
V
P
Q5
43
21
6
©G
lenc
oe/M
cGra
w-H
ill26
Gle
ncoe
Geo
met
ry
Perp
end
icu
lar
Lin
esL
ines
,ray
s,an
d se
gmen
ts t
hat
form
fou
r ri
ght
angl
es a
re p
erp
end
icu
lar.
The
rig
ht a
ngle
sym
bol i
ndic
ates
tha
t th
e lin
es
are
perp
endi
cula
r.In
the
fig
ure
at t
he r
ight
,AC
! "#
is p
erpe
ndic
ular
to
BD
!"# ,
or A
C! "
#!
BD
!"# .
Fin
d x
so t
hat
D !Z!
!P!
Z!.
If D !
Z!!
P!Z!,t
hen
m"
DZ
P$
90.
m"
DZ
Q#
m"
QZ
P$
m"
DZ
PS
um o
f par
ts $
who
le
(9x
#5)
#(3
x#
1)$
90S
ubst
itutio
n
12x
#6
$90
Sim
plify
.12
x$
84S
ubtr
act 6
from
eac
h si
de.
x$
7D
ivid
e ea
ch s
ide
by 1
2.
1.F
ind
xan
d y
so t
hat
NR
!"#
!M
Q!"
# .x
$15
,y$
8
2.F
ind
m"
MS
N.9
0
3.m
"E
BF
$3x
#10
,m"
DB
E$
x,an
d B
D""
#!
BF
""# .
Fin
d x.
x$
20
4.If
m"
EB
F$
7y!
3 an
d m
"F
BC
$3y
#3,
find
yso
th
at E
B" "
# !B
C""
# .9
5.F
ind
x,m
"P
QS,
and
m"
SQ
R.
x$
8,m
!P
QS
$24
,m!
SQ
R$
66
6.F
ind
y,m
"R
PT,
and
m"
TP
W.
y$
15,m
!R
PT
$55
,m!
TPW
$35
P
S
V
R
W
T(4
y #
5)%
(2y
" 5
)%QR
PS
3x% (8
x "
2)%
BC
A
DE
F
M
N RSQP
x%5x
%
(9y
" 1
8)%
Z
D
P
Q(9
x "
5)% (3
x "
1)%
B CDA
Stu
dy
Gu
ide
and I
nte
rven
tion
(con
tinu
ed)
Ang
le R
elat
ions
hips
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
PE
RIO
D__
___
1-5
1-5
Exam
ple
Exam
ple
Exercis
esExercis
es
Answers (Lesson 1-5)
© Glencoe/McGraw-Hill A15 Glencoe Geometry
An
swer
s
Skil
ls P
ract
ice
Ang
le R
elat
ions
hips
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
PE
RIO
D__
___
1-5
1-5
©G
lenc
oe/M
cGra
w-H
ill27
Gle
ncoe
Geo
met
ry
Lesson 1-5
For
Exe
rcis
es 1
–6,u
se t
he
figu
re a
t th
e ri
ght
and
a
pro
trac
tor.
1.N
ame
two
acut
e ve
rtic
al a
ngle
s.!
EK
H,!
FKG
2.N
ame
two
obtu
se v
erti
cal a
ngle
s.!
EK
F,!
HK
G
3.N
ame
a lin
ear
pair
.S
ampl
e an
swer
:!E
KH
,!E
KF
4.N
ame
two
acut
e ad
jace
nt a
ngle
s.!
FKG
,!G
KJ
5.N
ame
an a
ngle
com
plem
enta
ry t
o "
EK
H.
!G
KJ
6.N
ame
an a
ngle
sup
plem
enta
ry t
o "
FK
G.
!E
KF
or !
GK
H
7.F
ind
the
mea
sure
s of
an
angl
e an
d it
s co
mpl
emen
t if
one
ang
le m
easu
res
18 d
egre
esm
ore
than
the
oth
er.
36,5
4
8.T
he m
easu
re o
f th
e su
pple
men
t of
an
angl
e is
36
less
tha
n th
e m
easu
re o
f th
e an
gle.
Fin
d th
e m
easu
res
of t
he a
ngle
s.72
,108
ALG
EBR
AF
or E
xerc
ises
9–1
0,u
se t
he
figu
re a
t th
e ri
ght.
9.If
m"
RT
S$
8x#
18,f
ind
xso
tha
t T
R""
#!
TS
""# .
9
10.I
f m
"P
TQ
$3y
!10
and
m"
QT
R$
y,fi
nd y
so t
hat
"P
TR
is a
rig
ht a
ngle
.25
Det
erm
ine
wh
eth
er e
ach
sta
tem
ent
can
be
assu
med
fr
om t
he
figu
re.E
xpla
in.
11."
WZ
Uis
a r
ight
ang
le.
Yes;
it is
mar
ked
with
a r
ight
ang
le s
ymbo
l.
12."
YZ
Uan
d "
UZ
V a
re s
uppl
emen
tary
.
Yes;
the
sum
of
thei
r m
easu
res
is 1
80 s
ince
the
an
gles
form
a li
near
pai
r.
13."
VZ
Uis
adj
acen
t to
"Y
ZX
.
No;
the
angl
es d
o no
t sh
are
a co
mm
on s
ide.
ZX
W
V
YU
TP
QR
S
K
G
J
FE H
©G
lenc
oe/M
cGra
w-H
ill28
Gle
ncoe
Geo
met
ry
For
Exe
rcis
es 1
–4,u
se t
he
figu
re a
t th
e ri
ght
and
a
pro
trac
tor.
1.N
ame
two
obtu
se v
erti
cal a
ngle
s.
Sam
ple
answ
er:!
GFH
,!C
FE2.
Nam
e a
linea
r pa
ir w
hose
ver
tex
is B
.!
GB
C,!
CB
A
3.N
ame
an a
ngle
not
adj
acen
t to
but
com
plem
enta
ry t
o "
FG
C.
!FE
D
4.N
ame
an a
ngle
adj
acen
t an
d su
pple
men
tary
to
"D
CB
.!
BC
Gor
!D
CH
5.T
wo
angl
es a
re c
ompl
emen
tary
.The
mea
sure
of
one
angl
e is
21
mor
e th
an t
wic
e th
em
easu
re o
f th
e ot
her
angl
e.F
ind
the
mea
sure
s of
the
ang
les.
23,6
7
6.If
a s
uppl
emen
t of
an
angl
e ha
s a
mea
sure
78
less
tha
n th
e m
easu
re o
f th
e an
gle,
wha
tar
e th
e m
easu
res
of t
he a
ngle
s?12
9,51
AL
GE
BR
AF
or E
xerc
ises
7–8
,use
th
e fi
gure
at
the
righ
t.
7.If
m"
FG
E$
5x#
10,f
ind
xso
tha
t F
C! "
#!
AE
!"# .
16
8.If
m"
BG
C$
16x
!4
and
m"
CG
D$
2x#
13,
find
xso
tha
t "
BG
Dis
a r
ight
ang
le.
4.5
Det
erm
ine
wh
eth
er e
ach
sta
tem
ent
can
be
assu
med
fro
m t
he
figu
re.E
xpla
in.
9."
NQ
Oan
d "
OQ
Par
e co
mpl
emen
tary
.
No;
m!
NQ
Pis
not
kno
wn
to b
e 90
.
10."
SR
Qan
d "
QR
Pis
a li
near
pai
r.Ye
s;th
ey a
re a
djac
ent
angl
es w
hose
non
com
mon
sid
es a
re o
ppos
ite r
ays.
11."
MQ
Nan
d "
MQ
Rar
e ve
rtic
al a
ngle
s.
No;
the
angl
es a
re a
djac
ent.
12.S
TREE
T M
APS
Dar
ren
sket
ched
a m
ap o
f th
e cr
oss
stre
ets
near
est
to h
is h
ome
for
his
frie
nd M
igue
l.D
escr
ibe
two
diff
eren
t an
gle
rela
tion
ship
s be
twee
n th
e st
reet
s.
Sam
ple
answ
er:B
eaco
n !
Mai
n;O
live
divi
des
two
of t
hean
gles
form
ed b
y B
acon
and
Mai
n in
to p
airs
of
com
plem
enta
ry a
ngle
s.
Oliv
e
Beacon
Main
Q
O
P
RS
M
N
GF
AB
E
D
C
DA
E
HG
BC
F
Pra
ctic
e (A
vera
ge)
Ang
le R
elat
ions
hips
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
PE
RIO
D__
___
1-5
1-5
Answers (Lesson 1-5)
© Glencoe/McGraw-Hill A16 Glencoe Geometry
Rea
din
g t
o L
earn
Math
emati
csA
ngle
Rel
atio
nshi
ps
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
PE
RIO
D__
___
1-5
1-5
©G
lenc
oe/M
cGra
w-H
ill29
Gle
ncoe
Geo
met
ry
Lesson 1-5
Pre-
Act
ivit
yW
hat
kin
ds
of a
ngl
es a
re f
orm
ed w
hen
str
eets
in
ters
ect?
Rea
d th
e in
trod
ucti
on t
o L
esso
n 1-
5 at
the
top
of
page
37
in y
our
text
book
.•
How
man
y se
para
te a
ngle
s ar
e fo
rmed
if t
hree
line
s in
ters
ect
at a
com
mon
poin
t? (D
o no
t us
e an
ang
le w
hose
inte
rior
incl
udes
par
t of
ano
ther
ang
le.)
6•
How
man
y se
para
te a
ngle
s ar
e fo
rmed
if n
lines
inte
rsec
t at
a c
omm
onpo
int?
(Do
not
coun
t an
ang
le w
hose
inte
rior
incl
udes
par
t of
ano
ther
ang
le.)
2n
Rea
din
g t
he
Less
on
1.N
ame
each
of
the
follo
win
g in
the
fig
ure
at t
he r
ight
.a.
two
pair
s of
con
grue
nt a
ngle
s!
1 an
d !
3,!
2 an
d !
4b.
a pa
ir o
f ac
ute
vert
ical
ang
les
!2
and
!4
c.a
pair
of
obtu
se v
erti
cal a
ngle
s!
1 an
d !
3d.
four
pai
rs o
f ad
jace
nt a
ngle
s!
1 an
d !
2,!
2 an
d !
3,!
3 an
d !
4,!
4 an
d !
1e.
two
pair
s of
ver
tica
l ang
les
!1
and
!3,
!2
and
!4
f.fo
ur li
near
pai
rs!
1 an
d !
2,!
2 an
d !
3,!
3 an
d !
4,!
4 an
d !
1g.
four
pai
rs o
f su
pple
men
tary
ang
les
!1
and
!2,
!2
and
!3,
!3
and
!4,
!4
and
!1
2.Te
ll w
heth
er e
ach
stat
emen
t is
alw
ays,
som
etim
es,o
r ne
ver
true
.a.
If t
wo
angl
es a
re a
djac
ent
angl
es,t
hey
form
a li
near
pai
r.so
met
imes
b.If
tw
o an
gles
for
m a
line
ar p
air,
they
are
com
plem
enta
ry.
neve
rc.
If t
wo
angl
es a
re s
uppl
emen
tary
,the
y ar
e co
ngru
ent.
som
etim
esd.
If t
wo
angl
es a
re c
ompl
emen
tary
,the
y ar
e ad
jace
nt.
som
etim
ese.
Whe
n tw
o pe
rpen
dicu
lar
lines
inte
rsec
t,fo
ur c
ongr
uent
ang
les
are
form
ed.
alw
ays
f.V
erti
cal a
ngle
s ar
e su
pple
men
tary
.so
met
imes
g.V
erti
cal a
ngle
s ar
e co
mpl
emen
tary
.so
met
imes
h.
The
tw
o an
gles
in a
line
ar p
air
are
both
acu
te.
neve
ri.
If t
wo
angl
es f
orm
a li
near
pai
r,on
e is
acu
te a
nd t
he o
ther
is o
btus
e.so
met
imes
3.C
ompl
ete
each
sen
tenc
e.a.
If t
wo
angl
es a
re s
uppl
emen
tary
and
xis
the
mea
sure
of
one
of t
he a
ngle
s,th
en t
hem
easu
re o
f th
e ot
her
angl
e is
.
b.If
tw
o an
gles
are
com
plem
enta
ry a
nd x
is t
he m
easu
re o
f on
e of
the
ang
les,
then
the
mea
sure
of
the
othe
r an
gle
is
.
Hel
pin
g Y
ou
Rem
emb
er4.
Loo
k up
the
non
mat
hem
atic
al m
eani
ng o
f sup
plem
enta
ryin
you
r di
ctio
nary
.How
can
this
def
init
ion
help
you
to
rem
embe
r th
e m
eani
ng o
f su
pple
men
tary
ang
les?
Sam
ple
answ
er:S
uppl
emen
tary
mea
ns s
omet
hing
add
ed t
o co
mpl
ete
a th
ing.
An
angl
e an
d its
sup
plem
ent
can
be jo
ined
to
obta
in a
line
ar p
air.
90 #
x
180
#x
65%
23
41
©G
lenc
oe/M
cGra
w-H
ill30
Gle
ncoe
Geo
met
ry
Cur
ve S
titch
ing
The
sta
r de
sign
at
the
righ
t w
as c
reat
ed b
y a
met
hod
know
n as
cu
rve
stit
chin
g.A
ltho
ugh
the
desi
gn a
ppea
rs t
o co
ntai
n cu
rves
,it
is m
ade
up
enti
rely
of
line
segm
ents
.
To b
egin
the
sta
r de
sign
,dra
w a
60°
angl
e.M
ark
eigh
t eq
ually
-spa
ced
poin
ts o
n ea
ch r
ay,a
nd
num
ber
the
poin
ts a
s sh
own
belo
w.T
hen
conn
ect
pair
s of
poi
nts
that
hav
e th
e sa
me
num
ber.
To m
ake
a co
mpl
ete
star
,mak
e th
e sa
me
desi
gn in
si
x 60
°an
gles
tha
t ha
ve a
com
mon
cen
tral
ver
tex.
1.C
ompl
ete
the
sect
ion
of t
he s
tar
desi
gn a
bove
by
conn
ecti
ng
pair
s of
poi
nts
that
hav
e th
e sa
me
num
ber.
2.C
ompl
ete
the
follo
win
g de
sign
.
3.C
reat
e yo
ur o
wn
desi
gn.Y
ou m
ay u
se s
ever
al a
ngle
s,an
d th
e an
gles
may
ove
rlap
.S
ee s
tude
nts’
wor
k.
12
34
56
78
9
11
11
12
13
14
15
16
17
18
19
1
2
3
4
5
6
7
8
9
1213
1415
1617
1819
8
7
6
5
4
3
2
1
12
34
56
78
En
rich
men
t
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
PE
RIO
D__
___
1-5
1-5
Answers (Lesson 1-5)
© Glencoe/McGraw-Hill A17 Glencoe Geometry
An
swer
s
Answers (Lesson 1-6)
Stu
dy
Gu
ide
and I
nte
rven
tion
Poly
gons
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
PE
RIO
D__
___
1-6
1-6
©G
lenc
oe/M
cGra
w-H
ill31
Gle
ncoe
Geo
met
ry
Lesson 1-6
Poly
go
ns
A p
olyg
onis
a c
lose
d fi
gure
for
med
by
a fi
nite
num
ber
of c
opla
nar
line
segm
ents
.The
sid
es t
hat
have
a c
omm
on e
ndpo
int
mus
t be
non
colli
near
and
eac
h si
dein
ters
ects
exa
ctly
tw
o ot
her
side
s at
the
ir e
ndpo
ints
.A p
olyg
on is
nam
ed a
ccor
ding
to
its
num
ber
of s
ides
.A r
egu
lar
pol
ygon
has
cong
ruen
t si
des
and
cong
ruen
t an
gles
.A p
olyg
onca
n be
con
cave
or c
onve
x.
Nam
e ea
ch p
olyg
on b
y it
s n
um
ber
of s
ides
.Th
en c
lass
ify
it a
sco
nca
veor
con
vex
and
reg
ula
ror
irr
egu
lar.
Exam
ple
Exam
ple
a.
The
pol
ygon
has
4 s
ides
,so
it is
a q
uadr
ilate
ral.
It is
con
cave
bec
ause
par
t of
D !E!
or E!
F!lie
s in
the
inte
rior
of
the
figu
re.B
ecau
se it
is c
onca
ve,i
tca
nnot
hav
e al
l its
ang
les
cong
ruen
t an
d so
it is
irre
gula
r.
c.
The
pol
ygon
has
5 s
ides
,so
it is
a p
enta
gon.
It is
conv
ex.A
ll si
des
are
cong
ruen
t an
d al
l ang
les
are
cong
ruen
t,so
it is
a r
egul
ar p
enta
gon.
DF
GEb.
The
fig
ure
is n
ot c
lose
d,so
it is
not
a po
lygo
n.
d.
The
fig
ure
has
8 co
ngru
ent
side
san
d 8
cong
ruen
t an
gles
.It
isco
nvex
and
is a
reg
ular
oct
agon
.
H
JK
LI
Exercis
esExercis
es
Nam
e ea
ch p
olyg
on b
y it
s n
um
ber
of s
ides
.Th
en c
lass
ify
it a
s co
nca
veor
con
vex
and
reg
ula
ror
irr
egu
lar.
1.2.
3.
hexa
gon;
conv
ex;
quad
rila
tera
l;co
nvex
;pe
ntag
on;c
onca
ve;
regu
lar
irre
gula
rir
regu
lar
4.5.
6.
tria
ngle
;con
vex;
pent
agon
;con
cave
;oc
tago
n;co
ncav
e;ir
regu
lar
irre
gula
rir
regu
lar
©G
lenc
oe/M
cGra
w-H
ill32
Gle
ncoe
Geo
met
ry
Peri
met
erT
he p
erim
eter
of a
pol
ygon
is t
he s
um o
f th
e le
ngth
s of
all
the
side
s of
the
poly
gon.
The
re a
re s
peci
al f
orm
ulas
for
the
per
imet
er o
f a
squa
re o
r a
rect
angl
e.
Wri
te a
n e
xpre
ssio
n o
r fo
rmu
la f
or t
he
per
imet
er o
f ea
ch p
olyg
on.
Fin
d t
he
per
imet
er.
Stu
dy
Gu
ide
and I
nte
rven
tion
(con
tinu
ed)
Poly
gons
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
PE
RIO
D__
___
1-6
1-6
Exam
ple
Exam
ple
a.
P!
a"
b"
c!
3 "
4 "
5!
12 in
.
b.
P!
4s!
4(5)
!20
cm
c.
P!
2 !"
2w!
2(3)
"2(
2)!
10 f
t
3 ft
2 ft
! !
ww
5 cm
5 cm
5 cm
5 cms s
ss
3 in
.5
in.
4 in
.
a
b c
Exercis
esExercis
es
Fin
d t
he
per
imet
er o
f ea
ch f
igu
re.
1.2.
9 cm
22 f
t
3.4.
96 y
d10
cm
Fin
d t
he
len
gth
of
each
sid
e of
th
e p
olyg
on f
or t
he
give
n p
erim
eter
.
5.P
!96
6.P
!48
16,3
28,
10,1
0,20
x
x
2x
x !
2
rect
angl
e
2x
x
1 cm
24 y
d
19 y
d
12 y
d14
yd
27 y
d
squa
re
5.5
ft
3.5
cm
3 cm
2.5
cm
© Glencoe/McGraw-Hill A18 Glencoe Geometry
Skil
ls P
ract
ice
Poly
gons
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
PE
RIO
D__
___
1-6
1-6
©G
lenc
oe/M
cGra
w-H
ill33
Gle
ncoe
Geo
met
ry
Lesson 1-6
Nam
e ea
ch p
olyg
on b
y it
s n
um
ber
of s
ides
an
d t
hen
cla
ssif
y it
as
con
vex
orco
nca
vean
d r
egu
lar
or i
rreg
ula
r.
1.2.
3.
quad
rila
tera
l;co
nvex
;tr
iang
le;c
onve
x;pe
ntag
on;c
onca
ve;
irre
gula
rre
gula
rir
regu
lar
4.5.
6.
hept
agon
;con
vex;
quad
rila
tera
l;co
nvex
;do
deca
gon;
regu
lar
irre
gula
rco
ncav
e;ir
regu
lar
Fin
d t
he
per
imet
er o
f ea
ch f
igu
re.
7.8.
9.
98 y
d20
m32
in.
CO
OR
DIN
ATE
GEO
MET
RYF
ind
th
e p
erim
eter
of
each
pol
ygon
.
10.t
rian
gle
AB
Cw
ith
vert
ices
A(3
,5),
B(3
,1),
and
C(0
,1)
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nits
11.q
uadr
ilate
ral Q
RS
Tw
ith
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ices
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3,2)
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3,!
4)
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nits
12.q
uadr
ilate
ral L
MN
Ow
ith
vert
ices
L(!
1,4)
,M(3
,4),
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nits
ALG
EBR
AF
ind
th
e le
ngt
h o
f ea
ch s
ide
of t
he
pol
ygon
for
th
e gi
ven
per
imet
er.
13.P
$10
4 m
illim
eter
s14
.P$
84 k
ilom
eter
s15
.P$
88 f
eet
All
are
13 m
m.
All
are
28 k
m.
9 ft
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t,35
ft,
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t
4w #
1
w
10 in
.
10 in
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in.
2 in
.
2 in
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in.
2 in
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in.
5 m
2 m
3 m
6 m
4 m
40 y
d
20 y
d
18 y
d20
yd
©G
lenc
oe/M
cGra
w-H
ill34
Gle
ncoe
Geo
met
ry
Nam
e ea
ch p
olyg
on b
y it
s n
um
ber
of s
ides
an
d t
hen
cla
ssif
y it
as
con
vex
orco
nca
vean
d r
egu
lar
or i
rreg
ula
r.
1.2.
3.
hexa
gon;
conc
ave;
nona
gon;
conv
ex;
quad
rila
tera
l;ir
regu
lar
regu
lar
conv
ex;i
rreg
ular
Fin
d t
he
per
imet
er o
f ea
ch f
igu
re.
4.5.
6.
53 m
m86
mi
56 c
m
CO
OR
DIN
ATE
GEO
MET
RYF
ind
th
e p
erim
eter
of
each
pol
ygon
.
7.qu
adri
late
ral O
PQ
Rw
ith
vert
ices
O(!
3,2)
,P(1
,5),
Q(6
,4),
and
R(5
,!2)
$25
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nits
8.pe
ntag
on S
TU
VW
wit
h ve
rtic
es S
(0,0
),T
(3,!
2),U
(2,!
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(!2,
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2)
$17
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nits
ALG
EBR
AF
ind
th
e le
ngt
h o
f ea
ch s
ide
of t
he
pol
ygon
for
th
e gi
ven
per
imet
er.
9.P
$26
inch
es10
.P$
39 c
enti
met
ers
11.P
$89
fee
t
3 in
.,3
in.,
10 in
.,10
in.
17 c
m,1
7 cm
,5 c
m18
ft,
18 f
t,36
ft,
17 f
t
SEW
ING
For
Exe
rcis
es 1
2–13
,use
th
e fo
llow
ing
info
rmat
ion
.Ja
smin
e pl
ans
to s
ew f
ring
e ar
ound
the
sca
rf s
how
n in
the
dia
gram
.
12.H
ow m
any
inch
es o
f fr
inge
doe
s sh
e ne
ed t
o pu
rcha
se?
40 in
.
13.I
f Ja
smin
e do
uble
s th
e w
idth
of
the
scar
f,ho
w m
any
inch
es o
f fr
inge
will
she
nee
d?
48 in
.
16 in
.
4 in
.4
in.
16 in
.
2x "
2
x "
9
5x #
4
3x "
52x
# 3
6n #
8
n
14 c
m
14 c
m
4 cm
4 cm
6 cm
6 cm
6 cm
2 cm
32 m
i33 m
i21
mi
7 m
m
10 m
m18
mm
18 m
m
Pra
ctic
e (A
vera
ge)
Poly
gons
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
PE
RIO
D__
___
1-6
1-6
Answers (Lesson 1-6)
© Glencoe/McGraw-Hill A19 Glencoe Geometry
An
swer
s
Rea
din
g t
o L
earn
Math
emati
csPo
lygo
ns
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
PE
RIO
D__
___
1-6
1-6
©G
lenc
oe/M
cGra
w-H
ill35
Gle
ncoe
Geo
met
ry
Lesson 1-6
Pre-
Act
ivit
yH
ow a
re p
olyg
ons
rela
ted
to
toys
?
Rea
d th
e in
trod
ucti
on t
o L
esso
n 1-
6 at
the
top
of
page
45
in y
our
text
book
.
Nam
e fo
ur d
iffer
ent
shap
es t
hat
can
each
be
form
ed b
y fo
ur s
tick
s co
nnec
ted
tofo
rm a
clo
sed
figu
re.A
ssum
e yo
u ha
ve s
tick
s w
ith
a go
od v
arie
ty o
f le
ngth
s.S
ampl
e an
swer
:squ
are,
rect
angl
e,pa
ralle
logr
am,t
rape
zoid
Rea
din
g t
he
Less
on
1.Te
ll w
hy e
ach
figu
re is
not
a po
lygo
n.a.
b.c.
not
clos
edcu
rved
(no
t al
l mad
eS
ides
inte
rsec
t at a
poi
ntup
of
segm
ents
)th
at is
not
an
endp
oint
.
2.N
ame
each
pol
ygon
by
its
num
ber
of s
ides
.The
n cl
assi
fy it
as
conv
exor
con
cave
and
regu
lar
or n
ot r
egul
ar.
a.b.
c.
pent
agon
,con
vex,
quad
rila
tera
l,qu
adri
late
ral,
conv
ex,
regu
lar
conc
ave,
not
regu
lar
not
regu
lar
3.W
hat
is a
noth
er n
ame
for
a re
gula
r qu
adri
late
ral?
a sq
uare
4.M
atch
eac
h po
lygo
n in
the
fir
st c
olum
n w
ith
the
form
ula
in t
he s
econ
d co
lum
n th
at c
anbe
use
d to
fin
d it
s pe
rim
eter
.(s
repr
esen
ts t
he le
ngth
of
each
sid
e of
a r
egul
ar p
olyg
on.)
a.re
gula
r do
deca
gon
ivi.
P$
8s
b.sq
uare
viii
.P$
6s
c.re
gula
r he
xago
nii
iii.
P$
a#
b#
c
d.re
ctan
gle
viv
.P
$12
s
e.re
gula
r oc
tago
ni
v.P
$2!
#2w
f.tr
iang
leiii
vi.P
$4s
Hel
pin
g Y
ou
Rem
emb
er
5.O
ne w
ay t
o re
mem
ber
the
mea
ning
of
a te
rm is
to
expl
ain
it t
o an
othe
r pe
rson
.H
ow w
ould
you
exp
lain
to
a fr
iend
wha
t a
regu
lar
poly
gon
is?
Sam
ple
answ
er:A
reg
ular
pol
ygon
look
s th
e sa
me
no m
atte
r w
hat
part
you
look
at.
The
side
s ar
e th
e sa
me
leng
th,a
nd t
he a
ngle
s ar
e th
e sa
me
size
.
©G
lenc
oe/M
cGra
w-H
ill36
Gle
ncoe
Geo
met
ry
En
rich
men
t
NA
ME
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__D
ATE
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PE
RIO
D__
___
1-6
1-6
Peri
met
er a
nd A
rea
of Ir
regu
lar
Sha
pes
Tw
o fo
rmul
as t
hat
are
used
fre
quen
tly
in m
athe
mat
ics
are
peri
met
er a
ndar
ea o
f a
rect
angl
e.
Per
imet
er:
P$
2 !#
2wA
rea:
A$
!w,w
here
!is
the
leng
th a
nd w
is t
he w
idth
How
ever
,man
y fi
gure
s ar
e co
mbi
nati
ons
of t
wo
or m
ore
rect
angl
es c
reat
ing
irre
gula
r sh
apes
.To
find
the
are
a of
an
irre
gula
r sh
ape,
it h
elps
to
sepa
rate
the
shap
e in
to r
ecta
ngle
s,ca
lcul
ate
the
form
ula
for
each
rec
tang
le,t
hen
find
the
sum
of
the
area
s.
Fin
d t
he
area
of
the
figu
re a
t th
e ri
ght.
Sepa
rate
the
fig
ure
into
tw
o re
ctan
gles
.
A$
!wA
1$
9*
2A
2$
3*
3$
18$
9
18#
9$
27
The
are
a of
the
irre
gula
r sh
ape
is 2
7 m
2 .
Fin
d t
he
area
an
d p
erim
eter
of
each
irr
egu
lar
shap
e.
1.2.
3.4.
For
Exe
rcis
es 5
–8,f
ind
th
e p
erim
eter
of
the
figu
res
in E
xerc
ises
1–4
.
5.6.
7.8.
9.D
escr
ibe
the
step
s yo
u us
ed t
o fi
nd t
he p
erim
eter
in E
xerc
ise
1.S
ee s
tude
nts’
wor
k.
48 f
t44
cm
96 m
17 in
.
A$
90 f
t2P
$46
ft
9 ft
2 ft
3 ft
7 ft
6 ft 4 ft
A$
40 c
m2
P$
44 c
m
8 cm
4 cm
2 cm
2 cm
4 cm
4 cm
6 cm
4 cm
A$
320
m2
P$
96 m
9 m
26 m
6 m
13 m
7 m
12 m
A$
12 in
2
P$
20 in
.
2 in
.
4 in
.4
in.
1 in
.
9 m
3 m
1
25
m
2 m
9 m
3 m
5 m
2 m
Exam
ple
Exam
ple
Answers (Lesson 1-6)