1. 2.6 Proving Statements about Angles

2. Properties of Angle Congruence ReflexiveFor any angle, A <A <A. SymmetricIf <A <B, then <B <A. TransitiveIf <A <B and <B <C, then <A <C.

3. Right Angle Congruence Theorem All right angles are congruent..... A B C X Y Z

4. Congruent Supplements Theorem If two angles are supplementary to the same angle, then they are congruent – If m<1 + m<2 = 180° and m<2 + m<3 = 180°, then m<1 = m<3 or

5. Congruent Complements Theorem If two angles are complementary to the same angle, then the two angles are congruent. – If m<4 + m<5 = 90° and m<5 + m<6 = 90°, then m<4 = m<6 or

6. Linear Pair Postulate If two angles form a linear pair, then they are supplementary. 12 m<1 + m<2 = 180°

7. Example: < 1 and < 2 are a linear pair. If m<1 = 78°, then find m<2.

8. Vertical Angles Theorem Vertical angles are congruent. 1 2 3 4

9. Example <1 and <2 are complementary angles. <1 and <3 are vertical angles. If m<3 = 49°, find m<2.

10. Proving the Right Angle Congruence Theorem Given: Angle 1 and angle 2 are right angles Prove: 1. Given 2. Def. of right  ’s 3. Trans. POE 4. Def. of   ’s StatementsReasons

11. Proving the Vertical Angles Theorem 5 6 7 Given:  5 and  6 are a linear pair.  6 and  7 are a linear pair. 1. Given 3.  Supplements Theorem Prove:  5   7 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. 2.Linear Pair Postulate StatementsReasons

12. Solve for x.

13. Give a reason for each step of the proof. Choose from the list of reasons given.

14. Given:  6   7 Prove:  5   8 Plan for Proof: First show that  5   6 and  7   8. Then use transitivity to show that  5   8.) 1. Given 4. Vertical  ’s Theorem 2. Vertical  ’s Theorem StatementsReasons 1.  6   7 4.  5   6 2.  7   8 3.  6   8 3. Trans. POC 5.  5   8 5. Trans. POC