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

Theorem 2.6: Vertical Angles Theorem Vertical angles are congruent. 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 3 1 4 1 ≅ 3; 2 ≅ 4

Proving Theorem 2.6 Statement: Given: 5 and 6 are a linear pair, 6 and 7 are a linear pair Prove: 5 7 5 7 6 Statement: 5 and 6 are a linear pair, 6 and 7 are a linear pair 5 and 6 are supplementary, 6 and 7 are supplementary 3. 5 ≅ 7 Reason: **Or you could go into measurements and prove it another way**