1. Geometry 2.7 Big Idea: Prove Angle Pair Big Idea: Prove Angle PairRelationships

2. Theorem 2.3: Right Angles Congruence Theorem All right angles are congruent.

3. Theorem 2.4: Congruent Supplements Theorem If two angles are supplementary to the same angle (or to congruent angles),then they are congruent.

4. Example If angles 1 and 3 are supplementary and angles 5 and 3 are supplementary, then angles 1 and 5 are congruent.

5. Theorem 2.5: Congruent Complements Theorem If two angles are complementary to the same angle (or to congruent angles),then they are congruent.

6. Example1 2 3 2 3 If angles 1 and 2 are complementary and angles 1 and 3 are complementary, then angles 2 and 3 are congruent.

7. Theorem 2.6: Vertical Angles Congruence Theorem Vertical angles are congruent.

8. Example 4 2 4 2 1 3 1 3

9. Postulate 12: Linear Pair Postulate If two angles form a linear pair, then they are supplementary.

10. Example Since angles 1 and 2 form a linear pair, they must be supplementary and m 1 + m 2 = 180º

11. Proof 1: Right Angles Congruence Theorem Given: PQR and UTS are right angles Prove: PQR UTS

12. StatementReason 1. 1. 2. m PQR = 90º;2. m UTS = 90º m UTS = 90º 3.m PQR = m UTS 3. 4.4. 5.5. Given: PQR and UTS are right angles Prove: PQR UTS

13. Example If m 1 = 112º, find the measure of angles 2, 3 & 4. If m 1 = 112º, find the measure of angles 2, 3 & 4.