introduction to geometry and geometric...
TRANSCRIPT
Chapter 9 Skills Practice • 695
© 2
011
Car
negi
e Le
arni
ng
Earth MeasureIntroduction to Geometry and Geometric Constructions
VocabularyWrite the term that best completes the statement.
1. means to have the same size, shape, and measure.
2. In geometry, a construction can also be called a(n) .
3. A(n) is a ruler with no numbers.
4. is the study of shapes and measurement.
5. When you a geometric figure, the figure is created with the use of tools
such as a ruler, straightedge, compass, or protractor.
6. are line segments that have the same length.
7. A(n) is described as a straight continuous arrangement of an infinite
number of points.
8. A(n) is part of a circle, or the curve between two points on a circle.
9. A(n) is a tool used to create arcs and circles.
10. When you a geometric figure, the figure is created without the use
of tools.
11. The point at which two or more lines or arcs intersect or cross is called a(n)
.
12. A(n) is described as a location in space, and it has no size or shape.
13. are two or more lines that are located in the same plane.
Lesson 9.1 Skills Practice
Name ________________________________________________________ Date _________________________
696 • Chapter 9 Skills Practice
© 2
011
Car
negi
e Le
arni
ng
Lesson 9.1 Skills Practice page 2
14. A(n) can be used to approximate the measure of an angle.
15. A(n) is a portion of a line that includes two points and the points
between those two points.
16. The points where a line segment begins and ends are called the .
17. When you a geometric figure, the figure is created using only a compass
and a straightedge.
18. A(n) is described as a flat surface with an infinite length and width
but no depth.
19. Lines that are not located in the same plane are called .
Problem SetMake a sketch and a drawing of each given figure.
1.
DrawingSketch
Answers may vary.
2.
Chapter 9 Skills Practice • 697
© 2
011
Car
negi
e Le
arni
ng
Lesson 9.1 Skills Practice page 3
Name ________________________________________________________ Date _________________________
3.
4.
5.
698 • Chapter 9 Skills Practice
© 2
011
Car
negi
e Le
arni
ng
Lesson 9.1 Skills Practice page 4
6.
Construct each circle with the given radius and center.
7. Construct a circle using ___
AB as the radius and A as the center.
A B
Chapter 9 Skills Practice • 699
© 2
011
Car
negi
e Le
arni
ng
Lesson 9.1 Skills Practice page 5
Name ________________________________________________________ Date _________________________
8. Construct a circle using ___
CD as the radius and D as the center.
D
C
9. Construct a circle using ___
EF as the radius and F as the center.
E F
10. Construct a circle using ___
GH as the radius and H as the center.
H
G
700 • Chapter 9 Skills Practice
© 2
011
Car
negi
e Le
arni
ng
Lesson 9.1 Skills Practice page 6
11. Construct a circle using ___
JK as the radius and K as the center.
K
J
12. Construct a circle using ___
LM as the radius and L as the center.
L
M
Construct each arc using the given information.
13. Construct an arc using ___
AB as the radius and A as the center. Make the arc approximately one inch
long and make sure it does not pass through B.
Answers will vary.
A B
Chapter 9 Skills Practice • 701
© 2
011
Car
negi
e Le
arni
ng
Lesson 9.1 Skills Practice page 7
Name ________________________________________________________ Date _________________________
14. Construct an arc using ___
CD as the radius and D as the center. Make the arc approximately one inch
long and make sure it does not pass through C.
C D
15. Construct an arc using ___
EF as the radius and E as the center. Make the arc approximately one inch
long and make sure it does not pass through F.
F
E
16. Construct an arc using ___
GH as the radius and H as the center. Make the arc approximately one inch
long and make sure it passes through G.
H
G
702 • Chapter 9 Skills Practice
© 2
011
Car
negi
e Le
arni
ng
Lesson 9.1 Skills Practice page 8
17. Construct an arc using ___
JK as the radius and K as the center. Make the arc approximately one inch
long and make sure it passes through J.
J
K
18. Construct an arc using ___
LM as the radius and L as the center. Make the arc approximately one inch
long and make sure it passes through M.
L
M
Construct each line segment using the given information.
19. Duplicate ___
AB .
A B
A B
Chapter 9 Skills Practice • 703
© 2
011
Car
negi
e Le
arni
ng
Lesson 9.1 Skills Practice page 9
Name ________________________________________________________ Date _________________________
20. Duplicate ___
CD .
C D
21. Duplicate ___
EF .
E F
22. Construct a line segment that is twice the length of ___
JK .
J K
704 • Chapter 9 Skills Practice
© 2
011
Car
negi
e Le
arni
ng
23. Construct a line segment that is twice the length of ___
PQ .
P Q
24. Construct a line segment that is three times the length of ___
WX .
W X
Lesson 9.1 Skills Practice page 10
Chapter 9 Skills Practice • 705
© 2
011
Car
negi
e Le
arni
ng
Angles and More AnglesMeasuring and Constructing Angles
VocabularyMatch each definition to its corresponding term.
1. an angle whose measure is greater than 0°, but less
than 90°
a. ray
2. to divide into two equal parts b. angle
3. a portion of a line that begins at a point and extends
infinitely in one direction
c. vertex
4. a ray that is drawn through the vertex of an angle and
divides the angle into two congruent angles
d. sides of an angle
5. an angle whose measure is equal to 180° e. degrees
6. two rays that share a common endpoint to form
an angle
f. acute angle
7. a unit of measure for angles g. right angle
8. formed by two rays that share a common endpoint h. obtuse angle
9. an angle whose measure is greater than 90°, but less
than 180°
i. straight angle
10. the common endpoint of the two rays that form an angle j. congruent angles
11. two or more angles that have equal measures k. bisect
12. an angle whose measure is equal to 90° l. angle bisector
Lesson 9.2 Skills Practice
Name ________________________________________________________ Date _________________________
706 • Chapter 9 Skills Practice
© 2
011
Car
negi
e Le
arni
ng
Lesson 9.2 Skills Practice page 2
Problem SetUse a protractor to draw each angle with the given measure.
1. 40° angle 2. 150° angle
3. 75° angle 4. 110° angle
5. 160° angle 6. 25° angle
Chapter 9 Skills Practice • 707
© 2
011
Car
negi
e Le
arni
ng
Lesson 9.2 Skills Practice page 3
Name _______________________________________________________Date _________________________
7. 55° angle 8. 15° angle
Construct each angle using a compass and straightedge.
9. Construct an angle that is congruent to /A.
A A'
10. Construct an angle that is congruent to /B.
B
708 • Chapter 9 Skills Practice
© 2
011
Car
negi
e Le
arni
ng
Lesson 9.2 Skills Practice page 4
11. Construct an angle that is congruent to /C.
C
12. Construct an angle that is congruent to /D.
D
13. Construct an angle that is twice the measure of /E.
E
Chapter 9 Skills Practice • 709
© 2
011
Car
negi
e Le
arni
ng
Lesson 9.2 Skills Practice page 5
Name _______________________________________________________Date _________________________
14. Construct an angle that is twice the measure of /F.
F
Construct the angle bisector of each given angle using a compass and straightedge.
15. Construct the bisector of /G.
G
16. Construct the bisector of /H.
H
710 • Chapter 9 Skills Practice
© 2
011
Car
negi
e Le
arni
ng
Lesson 9.2 Skills Practice page 6
17. Construct the bisector of /J.
J
18. Construct the bisector of /K.
K
Chapter 9 Skills Practice • 711
© 2
011
Car
negi
e Le
arni
ng
Lesson 9.2 Skills Practice page 7
Name _______________________________________________________Date _________________________
19. Construct an angle that is one-fourth the measure of /M.
M
20. Construct an angle that is one-fourth the measure of /N.
N
712 • Chapter 9 Skills Practice
© 2
011
Car
negi
e Le
arni
ng
Chapter 9 Skills Practice • 713
© 2
011
Car
negi
e Le
arni
ng
Special AnglesComplements, Supplements, Midpoints, Perpendiculars, and Perpendicular Bisectors
VocabularyDraw an example of each term. Provide an explanation when necessary.
1. supplementary angles 2. complementary angles
3. perpendicular 4. midpoint of a segment
5. segment bisector 6. perpendicular bisector
Lesson 9.3 Skills Practice
Name _______________________________________________________Date _________________________
714 • Chapter 9 Skills Practice
© 2
011
Car
negi
e Le
arni
ng
Lesson 9.3 Skills Practice page 2
7. adjacent angles 8. linear pair
9. vertical angles
Problem SetCalculate the measure of an angle that is complementary to each given angle.
1. 30° angle 2. 70° angle
60°
3. 45° angle 4. 5° angle
5. 22° angle 6. 57° angle
7. 11° angle 8. 84° angle
Chapter 9 Skills Practice • 715
© 2
011
Car
negi
e Le
arni
ng
Lesson 9.3 Skills Practice page 3
Name _______________________________________________________Date _________________________
Calculate the measure of an angle that is supplementary to the given angle.
9. 60° angle 10. 100° angle
120°
11. 35° angle 12. 134° angle
13. 78° angle 14. 129° angle
15. 13° angle 16. 162° angle
Perform each given construction.
17. Construct a line perpendicular to the given line through point A.
A
716 • Chapter 9 Skills Practice
© 2
011
Car
negi
e Le
arni
ng
Lesson 9.3 Skills Practice page 4
18. Construct a line perpendicular to the given line through point B.
B
19. Construct a line perpendicular to the given line through point C.
C
Chapter 9 Skills Practice • 717
© 2
011
Car
negi
e Le
arni
ng
Lesson 9.3 Skills Practice page 5
Name _______________________________________________________Date _________________________
20. Construct a line perpendicular to the given line through point D.
D
21. Construct the perpendicular bisector of ___
EF .
E F
718 • Chapter 9 Skills Practice
© 2
011
Car
negi
e Le
arni
ng
Lesson 9.3 Skills Practice page 6
22. Construct the perpendicular bisector of ___
GH .
G H
23. Construct the midpoint of ___
JK .
J K
Chapter 9 Skills Practice • 719
© 2
011
Car
negi
e Le
arni
ng
Lesson 9.3 Skills Practice page 7
Name _______________________________________________________Date _________________________
24. Construct the midpoint of ___
LM .
L M
Identify the angle pairs in each given diagram.
25. Name all pairs of adjacent angles in the diagram shown.
/1 and /2, /2 and /3, /3 and /4, /4 and /1
1
423
720 • Chapter 9 Skills Practice
© 2
011
Car
negi
e Le
arni
ng
Lesson 9.3 Skills Practice page 8
26. Name all pairs of adjacent angles in the diagram shown.
5 67 8
27. Name all pairs of adjacent angles in the diagram shown.
9 1112
10
Chapter 9 Skills Practice • 721
© 2
011
Car
negi
e Le
arni
ng
Lesson 9.3 Skills Practice page 9
Name ________________________________________________________ Date _________________________
28. Name all pairs of adjacent angles in the diagram shown.
13 1416 15
29. Name all linear pairs in the diagram shown.
1
423
722 • Chapter 9 Skills Practice
© 2
011
Car
negi
e Le
arni
ng
Lesson 9.3 Skills Practice page 10
30. Name all linear pairs in the diagram shown.
5 67 8
31. Name all linear pairs in the diagram shown.
9 1112
10
Chapter 9 Skills Practice • 723
© 2
011
Car
negi
e Le
arni
ng
32. Name all linear pairs in the diagram shown.
13 1416 15
33. Name all vertical angle pairs in the diagram shown.
9 1112
100
Lesson 9.3 Skills Practice page 11
Name ________________________________________________________ Date _________________________
724 • Chapter 9 Skills Practice
© 2
011
Car
negi
e Le
arni
ng
34. Name all vertical angle pairs in the diagram shown.
13 1416 15
Lesson 9.3 Skills Practice page 12