EXAMPLE 3 Prove the Vertical Angles Congruence Theorem

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Presentation transcript:

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

Prove the Vertical Angles Congruence Theorem EXAMPLE 3 Prove the Vertical Angles Congruence Theorem STATEMENT REASONS 5 and 7 are vertical angles. 1. 1. Given 2. 5 and 7 are a linear pair. 6 and 7 are a linear pair. 2. Definition of linear pair, as shown in the diagram 3. 5 and 7 are supplementary. 6 and 7 are supplementary. 3. Linear Pair Postulate 4. ∠ 5 ∠ 7 Congruent Supplements Theorem 4.

GUIDED PRACTICE for Example 3 In Exercises 3–5, use the diagram. 3. If m 1 = 112°, find m 2, m 3, and m 4. ANSWER m 2 = 68° m 3 = 112° m 4 = 68°

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

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