Geometry/Trig 2 Name: __________________________
Unit 3 Review Packet Date: ___________________________
Section I – Name the three ways to prove that parallel lines exist.
1. ____________________________________________________________________
2. ____________________________________________________________________
3. ____________________________________________________________________
4. ____________________________________________________________________
5. ____________________________________________________________________
Section II – Identify the pairs of angles. If the angles have no relationship, write none.
1. 7 & 11 _________________________________
2. 3 & 6 _________________________________
3. 8 & 16 ________________________________
4. 2 & 7 _________________________________
5. 3 & 5 _________________________________
6. 1 & 6 __________________________________
7. 1 & 6 __________________________________
8. 1 & 4 __________________________________
Vertical angles are ______________________________________
If two parallel lines are cut by a transversal, then corresponding angles are ___________________
If two parallel lines are cut by a transversal, then alternate interior angles are _________________
If two parallel lines are cut by a transversal, then alternate exterior angles are ________________
If two parallel lines are cut by a transversal, then same side interior angles are ________________
If two parallel lines are cut by a transversal, then same side exterior angles are ________________
If two lines are perpendicular, then they form ______________, adjacent angles.
If two lines are parallel, then they are _________________ (A, S, N) skew.
A regular polygon is ________________ (A,S,N) equilateral.
The acute angles of a right triangle are ___________ (A,S,N) supplementary.
Section III – Fill In
Geometry/Trig 2 Name: __________________________
Unit 3 Review Packet – Page 2 Date: ___________________________
Section IV – Determine which lines, if any, are parallel based on the given information.
1 2
3 4
6
87
5
9 10
11 12
14
1615
13b
a1.) m1 = m9 _________________________
2.) m1 = m4 _________________________
3.) m12 + m14 = 180 _________________________
4.) m1 = m13 _________________________
5.) m7 = m14 _________________________
6.) m13 = m11 _________________________
7.) m15 + m16 = 180 _________________________
8.) m4 = m5 _________________________
Section IV – Determine which lines, if any, are parallel based on the given information.
312
45
6
87
9
10
111213
s
t
mkb
a
14
15
c d
1. m1 = m4 ___________________
2. m6 = m8 __________________
3. 1 and 11 are supplementary _______________
4. a ^ t and b ^ t ___________________________
5. m14 = m5 ______________________________
6. 6 and 7 are supplementary ________________
7. m14 = m15 ____________________________
8. 7 and 8 are supplementary _________________
9. m5 = m10 ______________________________
10. m1 = m13 ______________________________
Geometry/Trig 2 Name: __________________________
Unit 3 Review Packet – page 3 Date: ___________________________
Section V – Solve each Algebra Connection Problem.
1. 2.
4.3.
75
30
5x
x = _______
y = ________
w = _______
x = _______
y = _______
z = _______
x = _______
y = _______
37 2y
z + 57
w
x
4x - 5 23y
65 125
y
x + 12
6x 8x + 1
x = _______
6.5.4x + 13 4x + 25
6x6x
4x + 25 4x + 13
x = _______
A B
CD
x = _______
Is AB // DC? __________
Is AD // BC? __________
80
5x 4x + 17
83
10) ____ scalene right
11) ____ scalene acute
12) ____ scalene obtuse
13) ____ isosceles right
14) ____ isosceles acute
15) ____ isosceles obtuse
A) B) C)
D) E) F)
40°
80° 60°
80°
50° 50°
35°
35°
105°
45°
30°
Section II – Match each classification with the triangle that BEST suits it.
Number of Sides
Name of polygon
Sum of interior angles.
Measure of each interior
angle if it was a regular
polygon
Sum of the
Exterior Angles
Measure of each exterior angle if it
was a regular polygon.
Number of Diagonals that can be drawn.
3
4
5
6
7
8
9
10
n
Section II – Complete the chart.
Section VI – Answer each question regarding the given polygon.
30) Given a regular polygon with 6 sides, find:
31) The sum of the interior angles of this polygon is 900.
a) Name:
b) Sum of Interior Angles:
c) Sum of Exterior Angles:
d) Each Interior Angle:
e) Each exterior angle:
How many sides does this polygon have?
_______________________
What is the name of this polygon?
______________________
How many diagonals can be drawn in this polygon?
__________________
Section VII – Classify each polygon as convex or not convex; regular or irregular; name the polygon by number of sides. (Circle or fill in the appropriate answers).
34) 35) 36)
Convex OR Not Convex
Regular OR Irregular
Name: ____________________
Convex OR Not Convex
Regular OR Irregular
Name: ____________________
Convex OR Not Convex
Regular OR Irregular
Name: ____________________
32. ) Given a regular polygon with 6 sides, find:
a) Name:
b) Sum of Interior Angles:
c) Sum of Exterior Angles:
d) Each Interior Angle:
e) Each exterior angle:
32a.) Find the measure of one interior angle of a regular polygon with 18 sides:
b.) If each exterior angle of a regular polygon is 40 degrees, how many sides does it have?
c.) If each interior angle of a regular polygon is 72 degrees, how many sides does the polygon have?
Section V - Proofs
Statements Reasons
J
G K
IH
1. Given: GK bisects JGI; m3 = m2
Prove: GK // HI
1.
2.
3.
4.
5.
1. Given
2.
3. Given
4.
5.
Geometry/Trig 2 Name: __________________________
Unit 3 Review Packet – Page 3 Date: ___________________________
2
1
Statements Reasons
2. Given: AJ // CK; m1 = m5 Prove: BD // FE
1 2 3
4
5
A C
D
EF
B
J K
3
Statements Reasons
3. Given: a // b; 3 @ 4 Prove: 10 @ 11
3 4
5
6
7 8
910
2
b
a
c d
Geometry/Trig 2 Name: __________________________
Unit 3 Review Packet – Page 4 Date: ___________________________
1 3
54
6 7
28a
b
4. Given: 1 and 7 are supplementary.
Prove: m8 = m4
Statements Reasons
Geometry/Trig 2 Name: __________________________
Unit 3 Study Guide – Parallel Lines & Proofs
Section 3-1
Definitions:
Parallel Lines, Skew Lines, Parallel Planes, Parallel Line and Plane, Transversal, Alternate Interior Angles, Alternate Exterior Angles, Same Side Interior Angles, Corresponding Angles
Know How To:
1) Name figures described above.
2) Find the intersection of two figures.
3) Identify special pairs of angles
Suggested Exercises:
p. 75 #1-19; p. 76 #1-17; p. 77 #23-39
Section 3-2
Postulates and Theorems:1. If two parallel lines are cut by a transversal, then corresponding angles are congruent.
2. If two parallel lines are cut by a transversal, then alternate interior/exterior angles are congruent.
3. If two parallel lines are cut by a transversal, then same side interior angles are supplementary.
4. If a transversal is perpendicular to one of two parallel lines, then it is perpendicular to the other one also.
Know How To:
1) Use the statements above to complete proofs.
2) Find angle measures using the statements above.
3) Solve algebra connection problems using the statements above.
Suggested Exercises: p. 80 #1-13; p. 80-81 #1-16
Section 3-3
Know How To:
1.) Use these statements to complete proofs.
2.) Use these rules to determine whether given lines are parallel.
Suggested Exercises: p. 86 #1-11; p. 87 #1-19; p. 88 #24-26. p. 89 #1-16
You will be asked to name the 5 ways to prove that two lines are parallel. You may NOT use shorthand or abbreviations. They are:
1.) If two lines are cut by a transversal and corresponding angles are congruent, then the lines are parallel.
2.) If two lines are cut by a transversal and alternate interior/exterior angles are congruent, then the lines are parallel.
3.) If two lines are cut by a transversal and same side interior/exterior angles are supplementary, then the lines are parallel.
4.) If two lines are parallel to a third line, then the lines are parallel.
5.) If two lines are perpendicular to a third line, then the lines are parallel.