1. 1 2-5 Proving Angles Congruent Objectives: Identify relationships between angles that are: –Vertical –Complementary –Supplementary

2. 2 Recall: Angle Pairs – Vertical Angles Vertical Angles 1 2 3 4 Vertical angles:  1 and  3  2 and  4 A ngles V ertical

3. 3 Conjecture about Vertical Angles 1) On a sheet of paper, construct two intersecting lines that are not perpendicular. 2) With a protractor, measure each of the four angles formed. 3) Make a conjecture about vertical angles. 1 2 3 4

4. 4 Vertical Angles Theorem Vertical angles are congruent. 1 2 3 4  1 and  3 are congruent  2 and  4 are congruent

5. 5 Congruent Complements Theorem If two angles are congruent, then their complements are _________. The measure of angles complementary to  A and  B is 30. A B 60°  A   B congruent Recall: C omplementary Angles can be formed by C orner (90 degrees)

6. 6 Congruent Supplements Theorem Recall: S upplementary Angles can be formed by S traight Lines (180 degrees) If two angles are congruent, then their supplements are _________. The measure of angles supplementary to  1 and  4 is 110. 70° 4 3 2 1 110°  4   1 congruent