Objective: Find measures of complementary and supplementary angles

1. DO NOW: Find the value of x when km bisects LEKW. E M K W 3x 60 - 3x HOMEWORK: 2.1-2.3 Quiz Thursday 2.3 Practice worksheet A Objective: Find measures of complementary and supplementary angles

2. Homework check LABC; BD Twice 23o 70o 45o mLCBA = 35o; mLDBC = 70o mLCBA= 75o; mLDBC = 15o mLCBA = 45o; mLDBC = 90o x = 30 x = 20 x = 3 False True True True False 36o 2.2 Practice A

3. Homework check Midpoint Segment bisector Bisect TM = 7; MR = 7 FM = 18; MD = 18 MR = 5; QR = 10 KM = 10; KL = 20 (4, 2) (-3, 2) (3, -2) (1, 7) (-2, 1) X = 9 X = 8 250 cm 2.1 Practice A

4. Vocabulary Quiz • Take out your notes!

5. Important Terms • Complementary angles: Two angles whose sum equals 90o. • Complement: The angle that adds to the first angle to total 90o. • Supplementary angles: Two angles whose sum equals 180o. • Supplement: The angles that adds to the first angle to total 180o. • Adjacent Angles: Two angles that share a common vertex and side but have no common interior points. • Theorem: A true statement that follows from other true statements.

6. Follow up • Think of a way to help you remember the meaning of each term • Complementary angles: C and 90o • Supplementary angles: S and 180o

7. Example 1 State whether the angles are complementary, supplementary, or neither. A. B. C. Identify Angles 22o 158o 85o 15o 35o 55o

8. Solutions 180o; supplementary 100o; neither 90o; complementary Example 1

9. Example 2 State whether the numbered angles are adjacent or nonadjacent. a. b. c. Identify Adjacent Angles

10. Solutions Because the angles do not share a common vertex or side, L1 and L2 are nonadjacent. Because the angles share a common vertex and side, L3 and L4 are adjacent. Although L5 and L6 share a common vertex, they do not share a common side. Therefore, L5 and L6 are nonadjacent. Example 2

11. Example 3 LA is a complement of LC, and mLA = 47o. Find mLC. LP is a supplement of LR, and mLR = 36o. Find mLP. Complements and Supplements

12. Solution LAand LC are complements, so mLA + mLC= 90o. 47 + mLC = 90o.Substitute mLA. mLC = 43o. Solve for mLC. LP and LR, are supplements, so mLP = mLR= 180o mLP = 36o = 180oSubstitute for mLR. mLP = 144oSolve for mLP. Example 3

13. Checkpoint 30o 39o . . State whether the angles are complementary, supplementary, or neither. 49o 41o 32o 148o

14. Checkpoint 4. LB is a complement of LD, and mLD = 79o. Find mLB. 5. LG is a supplement of LH, and mLG = 115o. Find mLH. Continued…

15. Solutions Neither Complementary Supplementary . . Checkpoint

16. Theorem 2.1: Congruent Complements Theorem Words Symbols • If two angles are complementary to the same angle, then they are congruent. 2 3 1

17. Theorem 2.2: Congruent Supplements Theorem Words Symbols If two angles are supplementary to the same angle, then they are congruent.

18. Example 4 L7 and L8 are supplementary, and L8 and L9 are supplementary. Name a pair of congruent angles. Explain your reasoning. Use a Theorem 8 7 9

19. Solution L7 and L9 are both supplementary to L8. So, from the Congruent Supplements Theorem, it is true that L7 = L9. Example 4 ~

20. Checkpoint

21. Checkpoint In the diagram, mL10 + mL11 = 90o, and mL11 + mL12 = 90o. Name a pair of congruent angles. Explain your reasoning. Complete the following exercises 12 11 10

22. Solution Checkpoint