2.3 Complementary and Supplementary Angles

1. 2.3 Complementary and Supplementary Angles

2. Definitions • Complementary angles – the sum of their measures is 90˚ • Each angle is the compliment of the other A 32˚ 58˚ B

3. Definitions • Supplementary angles – the sum of their measures is 180˚ • Each angle is the supplement of the other 46˚ D 134˚ C

4. Identify Complements and Supplements 158˚ 22˚ 15˚ 85˚ 55˚ 35˚

5. Definitions • Adjacent angles – have a common vertex and side, but no common interior points Common side B Common vertex

6. Identify Adjacent Angles 3 4 5 6 1 2

7. Measures • m A is a complement of C, and m A = 47˚. Find m C. • 43˚ • M P is a supplement of R, and m R = 36˚. Find m P. • 144˚

8. Definitions • Theorem – a true statement that follows from other true statements

9. Theorem 2.1 Congruent Compliments Theorem • If two angles are complementary to the same angle, then they are congruent • m 1 + m 2 = 90˚ • m 3 + m 2 =90˚ • Then 1 3 1 2 3

10. Theorem 2.2 Congruent Supplements Theorem • If two angles are supplementary to the same angle, then they are congruent • m 1 + m 2 = 180˚ • m 3 + m 2 = 180˚ • Then 1 3 2 3 1

11. Use Theorems • 7 and 8 are supplementary • 8 and 9 are supplementary • Name a pair of congruent angles. • 7 9 8 7 9

12. Guided Practice • Pg. 70 #1-7