1. EXAMPLE 3
Prove the Vertical Angles Congruence Theorem
Prove vertical angles are congruent.
GIVEN:
5 and are vertical angles.
PROVE:
∠ 5 ∠ 7

2. Prove the Vertical Angles Congruence Theorem
EXAMPLE 3
Prove the Vertical Angles Congruence Theorem
STATEMENT
REASONS
5 and are vertical angles. 1. 1.
Given 2.
5 and are a linear pair.
6 and are a linear pair. 2.
Definition of linear pair, as shown in the diagram 3.
5 and are supplementary.
6 and are supplementary. 3.
Linear Pair Postulate 4.
∠ 5 ∠
Congruent Supplements Theorem 4.

3. GUIDED PRACTICE
for Example 3
In Exercises 3–5, use the diagram.
3. If m = 112°, find m 2, m 3, and m
ANSWER
m = 68°
m = 112°
m = 68°

4. GUIDED PRACTICE
for Example 3
4. If m = 67°, find m 1, m 3, and m
ANSWER
m = 113°
m = 113°
m = 67°
5. If m = 71°, find m 1, m 2, and m
ANSWER
m = 109°
m = 71°
m = 109°

5. GUIDED PRACTICE
for Example 3
6. Which previously proven theorem is used in Example 3 as a reason?
Congruent Supplements Theorem
ANSWER