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

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

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

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

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 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 ° °  4   1 congruent