+ Objective: Find measures of complementary and supplementary angles DO NOW: Find the value of x when km bisects LEKW. E M K W 3x x HOMEWORK: 1) Quiz Thursday 2)2.3 Practice worksheet A

+ Homework check 1) LABC; BD 2) Twice 3) 23 o 4) 70 o 5) 45 o 6) mLCBA = 35o; mLDBC = 70 o 7) mLCBA = 75o; mLDBC = 15 o 8) mLCBA = 45o; mLDBC = 90 o 9) x = 30 10) x = 20 11) x = 3 12) False 13) True 14) True 15) True 16) False 17) 36 o 2.2 Practice A

+ Homework check 1. Midpoint 2. Segment bisector 3. Bisect 4. TM = 7; MR = 7 5. FM = 18; MD = MR = 5; QR = KM = 10; KL = (4, 2) 9. (-3, 2) 10. (3, -2) 11. (1, 7) 12. (-2, 1) 13. X = X = cm 2.1 Practice A

+ Vocabulary Quiz Take out your notes!

+ Important Terms Complementary angles: Two angles whose sum equals 90 o. Complement: The angle that adds to the first angle to total 90 o. Supplementary angles: Two angles whose sum equals 180 o. Supplement: The angles that adds to the first angle to total 180 o. 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.

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

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

+ Solutions a. 180 o ; supplementary b. 100 o ; neither c. 90 o ; complementary Example 1

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

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

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

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

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

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

+ Solutions 1. Neither 2. Complementary 3. Supplementary Checkpoint

+ Theorem 2.1: Congruent Complements Theorem If two angles are complementary to the same angle, then they are congruent. WordsSymbols 1 23

+ Theorem 2.2: Congruent Supplements Theorem If two angles are supplementary to the same angle, then they are congruent. WordsSymbols

+ 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 79

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

+ Checkpoint

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

+ Solution Checkpoint