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Geometry/Trig
Name: __________________________
Unit 3 Review Packet – Answer Key
Date: ___________________________
Section I – Name the five ways to prove that parallel lines exist.
1. If corresponding angles are congruent, then lines are parallel.
2. If alternate interior angles are congruent, then lines are parallel.
3. If alternate exterior angles are congruent, then lines are parallel.
4. If same side interior angles are supplementary, then lines are parallel.
5. If same side exterior angles are supplementary, then lines are parallel.
Section II – Identify the pairs of angles. If the angles have no relationship, write none.
1. 7 & 11
None
2. 3 & 6
Alternate Interior Angles
3. 8 & 16
Corresponding Angles
4. 2 & 7
Alternate Exterior Angles
5. 3 & 5
Same Side Interior Angles
6. 1 & 6
None
7. 1 & 6
None
8. 1 & 4
Vertical Angles
1 2
3 4
a
b
5 6
7 8
Section III – Fill In
Vertical angles are congruent.
If lines are parallel, then corresponding angles are congruent.
If lines are parallel, then alternate interior angles are congruent.
If lines are parallel, then alternate exterior angles are congruent.
If lines are parallel, then same side interior angles are supplementary.
If lines are parallel, then same side exterior angles are supplementary.
9 10
11 12
13 14
15 16
Geometry/Trig
Name: __________________________
Unit 3 Review Packet – Page 2 – Answer Key
Date: ___________________________
Section IV – Determine which lines, if any, are parallel based on the given information.
1.) m1 = m9
c // d
2.) m1 = m4
None
3.) m12 + m14 = 180
a // b
4.) m1 = m13
None
5.) m7 = m14
c // d
6.) m13 = m11
None
7.) m15 + m16 = 180
None
8.) m4 = m5
a //b
1 2
3 4
a
b
5 6
7 8
c
9 10
11 12
13 14
15 16
d
Section IV – Determine which lines, if any, are parallel based on the given information.
1. m1 = m4
a // b
2. m6 = m8
t // s
3. 1 and 11 are supplementary
4. a ^ t and b ^ t
5. m14 = m5
None
a // b
a
None
b
6. 6 and 7 are supplementary t // s
7. m14 = m15
8. 7 and 8 are supplementary
9. m5 = m10
10. m1 = m13
k // m
None
m
15
13
k // m
k
12
11
9
8
10
None
1
2
3
4
14
5
6
t
7
s
Geometry/Trig
Name: __________________________
Unit 3 Review Packet – Page 3 – Answer Key
Date: ___________________________
J
Section V - Proofs
1. Given: GK bisects JGI; m3 = m2
G
Prove: GK // HI
Statements
1. GK bisects JGI
1
2
K
Reasons
1. Given
3
I
2. m1 = m2
2. Definition of an Angles Bisector
3. m3 = m2
3. Given
4. m1 = m3
4. Substitution
5. GK // HI
5. If corresponding angles are congruent, then the lines are
parallel.
2. Given: AJ // CK; m1 = m5
H
A
Prove: BD // FE
C
Reasons
Statements
1. AJ // CK
1. Given
2. m1 = m3
2. If lines are parallel, then
corresponding angles are
congruent.
3. m1 = m5
3. Given
4. m3 = m5
4. Substitution
5. BD // FE
5. If corresponding angles are
congruent, then the lines are
parallel.
1
B
F
2
4
5
J
K
3
D
E
Geometry/Trig
Name: __________________________
Unit 3 Review Packet – Page 4 – Answer Key
Date: ___________________________
3. Given: a // b; 3 @ 4
Statements
1. a // b
Prove: 10 @ 1
1
a
3
5
Reasons
6
1. Given
2. 4 @ 7
2. If lines are parallel then
alternate interior angles
are congruent.
3. 3 @ 4
3. Given
4. 3 @ 7
4. Substitution
5. 1 @ 3; 7 @ 10
5. Vertical Angles Theorem
6. 10 @ 1
6. Substitution
4. Given: 1 and 7 are supplementary.
Prove: m8 = m4
8
7
b
9
10
d
c
1
b
a
Statements
2
4
Reasons
4
6
8
3
5
7
2
1. 1 and 7 are supplementary
1. Given
2. m1 + m7 = 180
2. Definition of Supplementary Angles
3. m6 + m7 = 180
3. Angle Addition Postulate
4. m1 + m7 = m6 + m7
4. Substitution
5. m1 = m6
5. Subtraction Property
6. a // b
6. If corresponding angles are congruent, then the
lines are parallel.
7. m8 = m4
7. If lines are parallel, then corresponding angles are
congruent.
Geometry/Trig
Name: __________________________
Unit 3 Review Packet – Page 5 – Answer Key
Date: ___________________________
5. Given: ST // QR; 1 @ 3
Prove: 2 @ 3
P
Reasons
Statements
1. ST // QR
1. Given
2. 1 @ 2
2. If lines are parallel, then
corresponding angles are
congruent.
1
S
3. 1 @ 3
3. Given
4. 2 @ 3
4. Substitution
Q
3
T
2
R
6. Given: BE bisects DBA; 1 @ 3 Prove: CD // BE
Reasons
Statements
1. BE bisects DBA
1. Given
2. 2 @ 3
2. Definition of an Angle Bisector
3. 1 @ 3
3. Given
4. 2 @ 1
4. Substitution
5. CD // BE
5. If alternate interior angles are congruent, then the lines are
parallel.
C
B
2 3
1
D
E
A
Geometry/Trig
Name: __________________________
Unit 3 Review Packet – page 6 – Answer Key
Date: ___________________________
7.
Given: AB // CD; BC // DE
Reasons
Statements
Prove: 2 @ 6
1. AB // CD
1. Given
2. 2 @ 4
2. If lines are parallel, then alternate
interior angles are congruent.
3. BC // DE
3. Given
4. 4 @ 6
4. If lines are parallel, then alternate
interior angles are congruent.
5. 2 @ 6
5. Substitution
B
D
6
2
A
8.
1
3
5
7
C
E
Given: AB // CD; 2 @ 6
Reasons
Statements
4
Prove: BC // DE
1. AB // CD
1. Given
2. 2 @ 4
2. If lines are parallel, then alternate interior angles are congruent.
3. 2 @ 6
3. Given
4. 4 @ 6
4. Substitution
5. BC // DE
5. If alternate interior angles are congruent, then the lines are
parallel.
B
D
6
2
A
1
3
4
C
5
7
E
Geometry/Trig
Name: __________________________
Unit 3 Review Packet – page 7– Answer Key
Date: ___________________________
Section VI – Solve each Algebra Connection Problem.
1.
2.
w
4x - 5
z + 57
x
23y
65
37 2y
w = 37
Equations:
37 = w
x + 37 = 180
2y + 37 = 180
z + 57 = 143
x = 143
y = 71.5
125
Equations:
65 + 23y = 180
65 = 4x – 5
x = 17.5
y=5
z = 86
Equations:
30 + 75 = 5x
30 + 75 + y = 180
3.
30
Equation:
6x + x + 12 = 8x + 1
4.
x + 12
75
y
5x
6x
8x + 1
x = 21
y = 75
Section VII – Determine whether the given side lengths can create a triangle.
1) 7, 8, 9  YES
2) 7, 8, 15  NO
3) 7, 8, 14  YES
4) 3, 4, 5  YES
x = 11
Geometry/Trig
Name: __________________________
Unit 3 Review Packet – page 8
Date: ___________________________
Section VIII - Classify each triangle by its sides and by its angles.
1.
2.
A
D
3. G
04
9
B
F
C
K
4.
E
H
Scalene Right
Scalene Obtuse
L
5.
O
Scalene Acute
M
47
53
I
Scalene Acute
6.
60
36
J
60
Q
P
60
32
118
R
N
Equilateral Equiangular
7. In DABC which side is the longest? ___BC_____
Scalene Obtuse
the shortest? ______AC___
8. In DDEF which side is the longest? _DE___ the shortest? ___EF_______
9. In DGHI which side is the longest? ___HI_____
the shortest? _____GI____
10. In DJKL which side is the longest? ____JK____
the shortest? ____KL_____
11. In DMNO which side is the longest? ____all the same____
12. In DPQR which side is the longest? _QR____ the shortest___PR_____
In each triangle, name the smallest angle and the largest angle.
A
D
6.4
4.1
I
8
2.9
128
B
C
5.7
E
Smallest
<B
Smallest
Largest
<C
Largest
136
<E
<D
F
17.3
G
11
Smallest
Largest
H
<I
<G
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