1. 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. Ð7 & Ð None
2. Ð3 & Ð Alternate Interior Angles
3. Ð8 & Ð Corresponding Angles
4. Ð2 & Ð Alternate Exterior Angles
5. Ð3 & Ð Same Side Interior Angles
6. Ð1 & Ð None
7. Ð1 & Ð None
8. Ð1 & Ð Vertical Angles 1 2 9 10 a 3 4 11 12 5 6 13 14 b 7 8 15 16
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.

2. 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.) mÐ1 = mÐ9 c // d
2.) mÐ1 = mÐ4 None
3.) mÐ12 + mÐ14 = 180 a // b
4.) mÐ1 = mÐ13 None
5.) mÐ7 = mÐ14 c // d
6.) mÐ13 = mÐ11 None
7.) mÐ15 + mÐ16 = 180 None
8.) mÐ4 = mÐ5 a //b 1 2 9 10 a 3 4 11 12 5 6 13 14 b 7 8 15 16 c d
Section IV – Determine which lines, if any, are parallel based on the given information.
1. mÐ1 = mÐ4 a // b
2. mÐ6 = mÐ8 t // s
3. Ð1 and Ð11 are supplementary None
4. a ^ t and b ^ t a // b
5. mÐ14 = mÐ None
6. Ð6 and Ð7 are supplementary t // s
7. mÐ14 = mÐ k // m
8. Ð7 and Ð8 are supplementary None
9. mÐ5 = mÐ k // m
10. mÐ1 = mÐ13 None a b k m 15 t 13 12 11 9 8 7 10 2 5 1 3 4 6 s 14

3. Geometry/Trig Name: __________________________
Unit 3 Review Packet – Page 3 – Answer Key Date: ___________________________ J
Section V - Proofs
1. Given: GK bisects ÐJGI; mÐ3 = mÐ2
Prove: GK // HI 1 G K 2
Statements
Reasons
1. Given
1. GK bisects ÐJGI 3
2. mÐ1 = mÐ2
2. Definition of an Angles Bisector I H
3. mÐ3 = mÐ2
3. Given
4. mÐ1 = mÐ3
4. Substitution
5. GK // HI
5. If corresponding angles are congruent, then the lines are parallel.
2. Given: AJ // CK; mÐ1 = mÐ5 Prove: BD // FE A C
Reasons
Statements 1 2 3
1. AJ // CK 1. Given
2. mÐ1 = mÐ3 2. If lines are parallel, then corresponding angles are congruent.
3. mÐ1 = mÐ5 3. Given
4. mÐ3 = mÐ5 4. Substitution
5. BD // FE 5. If corresponding angles are congruent, then the lines are parallel. B D 4 5 F E J K

4. Geometry/Trig Name: __________________________
Unit 3 Review Packet – Page 4 – Answer Key Date: ___________________________
3. Given: a // b; Ð Prove: Ð1 1 2 a 3 4
Statements
Reasons 5 6
1. a // b 1. Given
2. Ð7 2. If lines are parallel then alternate interior angles are congruent.
3. Ð4 3. Given
4. Ð7 4. Substitution
5. Ð3; Ð10 5. Vertical Angles Theorem
6. Ð1 6. Substitution 7 8 b 10 9 c d
4. Given: Ð1 and Ð7 are supplementary.
Prove: mÐ8 = mÐ4 1 3 b 4 5 6 7 a
Statements
Reasons 8 2
1. Ð1 and Ð7 are supplementary 1. Given
2. mÐ1 + mÐ7 = Definition of Supplementary Angles
3. mÐ6 + mÐ7 = Angle Addition Postulate
4. mÐ1 + mÐ7 = mÐ6 + mÐ7 4. Substitution
5. mÐ1 = mÐ6 5. Subtraction Property
6. a // b 6. If corresponding angles are congruent, then the lines are parallel.
7. mÐ8 = mÐ4 7. If lines are parallel, then corresponding angles are congruent.

5. Geometry/Trig Name: __________________________
Unit 3 Review Packet – Page 5 – Answer Key Date: ___________________________
5. Given: ST // QR; Ð3 Prove: Ð3 P
Statements
Reasons
ST // QR 1. Given
2. Ð2 2. If lines are parallel, then corresponding angles are congruent.
3. Ð3 3. Given
4. Ð3 4. Substitution 1 3 S T 2 Q R
6. Given: BE bisects ÐDBA; Ð3 Prove: CD // BE
Statements
Reasons
1. BE bisects ÐDBA 1. Given
2. Ð3 2. Definition of an Angle Bisector
3. Ð3 3. Given
4. Ð1 4. Substitution
5. CD // BE 5. If alternate interior angles are congruent, then the lines are parallel. C B 2 3 1 A D E

6. Geometry/Trig Name: __________________________
Unit 3 Review Packet – page 6 – Answer Key Date: ___________________________ 7.
Given: AB // CD; BC // DE
Prove: Ð6
Statements
Reasons
1. AB // CD 1. Given
2. Ð4 2. If lines are parallel, then alternate interior angles are congruent.
3. BC // DE 3. Given
4. Ð6 4. If lines are parallel, then alternate interior angles are congruent.
5. Ð6 5. Substitution B D 2 6 4 1 3 5 7 A C E 8.
Given: AB // CD; Ð6
Prove: BC // DE
Statements
Reasons
1. AB // CD 1. Given
2. Ð4 2. If lines are parallel, then alternate interior angles are congruent.
3. Ð Given
4. Ð6 4. Substitution
5. BC // DE 5. If alternate interior angles are congruent, then the lines are parallel. B D 2 6 4 1 3 5 7 A C E

7. Section VI – Solve each Algebra Connection Problem.1. 2. w
4x - 5
23y
z + 57 x
65°
125°
37° 2y
Equations:
37 = w
x + 37 = 180
2y + 37 = 180
z + 57 = 143
w = 37
x = 143
y = 71.5
z = 86
Equations:
y = 180
65 = 4x – 5
x = 17.5
y = 5
Equations:
= 5x
y = 180
Equation:
6x + x + 12 = 8x + 1 3. 4.
30°
x + 12 y 5x
75° 6x
8x + 1
x = 21
y = 75
x = 11
Section VII - Classify each triangle by its sides and by its angles. 1. A 2. D 3. G
60°
100°
20°
59°
45° E F H B C I
Scalene
Acute
Isosceles
Right
Scalene
Obtuse 4. K 5. O 6. Q
42°
75° P
30°
55° J M
35° L N R
Scalene
Right
Scalene
Obtuse
Isosceles
Acute