2 6 Proving Statements about Angles Theorem 2

2. 6 Proving Statements about Angles

Theorem 2. 2 Properties of Angle Congruence Angle congruence is reflexive, symmetric, and transitive. Reflexive: For any angle A, A ≅ A. Symmetric If A ≅ B, then B ≅ A Transitive If A ≅ B and B ≅ C, then A ≅ C.

Some Theorems… Theorem 2. 3: All right angles are congruent. Theorem 2. 4: Congruent Supplements Theorem. If two angles are supplementary to the same angle (or to congruent angles), then they are congruent. Example: If m 1 + m 2 = 180 AND m 2 + m 3 = 180 , then m 1 = m 3 1 ≅ 3

Theorem 2. 5: Congruent Complements Theorem • If two angles are complementary to the same angle (or congruent angles), then the two angles are congruent. Example: If m 4 + m 5 = 90 AND m 5 + m 6 = 90 , then m 4 = m 6 4 ≅ 6

Postulate 12: Linear Pair Postulate If two angles form a linear pair, then they are supplementary. 1 2 m 1 + m 2 = 180 Theorem 2. 6: Vertical Angles Theorem Vertical angles are congruent. 2 1 3 4 1 ≅ 3; 2 ≅ 4

Proving Theorem 2. 6 Given: 5 and 6 are a linear pair, 6 and 7 are a linear pair Prove: 5 7 5 6 Statement: 1. 5 and 6 are a linear pair, 6 and 7 are a linear pair 2. 5 and 6 are supplementary, 6 and 7 are supplementary 3. 5 ≅ 7 7 Reason: 1. 2. 3. **Or you could go into measurements and prove it another way**