2.6 Proving Statements about Angles

1. 2.6 Proving Statements about Angles

2. Theorem 2.2 Properties of Angle Congruence

3. 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

4. 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

5. 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

6. Proving Theorem 2.6 5 7 Given: 5 and 6 are a linear pair, 6 and 7 are a linear pair Prove: 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**