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Objective: Find measures of complementary and supplementary angles

DO NOW: Find the value of x when km bisects LEKW.

E M

K W

3x 60 - 3x

HOMEWORK:1)2.1-2.3 Quiz

Thursday2)2.3 Practice

worksheet A

+Homework check

1) LABC; BD

2) Twice

3) 23o

4) 70o

5) 45o

6) mLCBA = 35o; mLDBC = 70o

7) mLCBA = 75o; mLDBC = 15o

8) mLCBA = 45o; mLDBC = 90o

9) x = 30

10) x = 20

11) x = 3

12) False

13) True

14) True

15) True

16) False

17) 36o

2.2 Practice A

+Homework check

1. Midpoint

2. Segment bisector

3. Bisect

4. TM = 7; MR = 7

5. FM = 18; MD = 18

6. MR = 5; QR = 10

7. KM = 10; KL = 20

8. (4, 2)

9. (-3, 2)

10. (3, -2)

11. (1, 7)

12. (-2, 1)

13. X = 9

14. X = 8

15. 250 cm

2.1 Practice A

+Vocabulary Quiz

Take out your notes!

+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.

+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

+Example 1

State whether the angles are complementary, supplementary, or neither.

A.

B.

C.

Identify Angles

22o 158o

15o85o

35o

55o

+Solutions

a. 180o; supplementary

b. 100o; neither

c. 90o; 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 = 47o. Find mLC.

b. LP is a supplement of LR, and mLR = 36o. Find mLP.

Complements and Supplements

+Solution

a. LA and LC are complements, so mLA + mLC = 90o.

47 + mLC = 90o. Substitute mLA.

mLC = 43o. Solve for mLC.

b. LP and LR, are supplements, so mLP = mLR = 180o

mLP = 36o = 180o Substitute for mLR.

mLP = 144o Solve for mLP.

Example 3

+Checkpoint

1. 30o 39o

2. .

3. .

State whether the angles are complementary, supplementary, or neither.

49o

41o

148o

32o

+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…

+Solutions

1. Neither

2. Complementary

3. Supplementary

4. .

5. .

Checkpoint

+Theorem 2.1: Congruent Complements Theorem

If two angles are complementary to the same angle, then they are congruent.

Words Symbols

12 3

+Theorem 2.2: Congruent Supplements Theorem

If two angles are supplementary to the same angle, then they are congruent.

Words Symbols

+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

87 9

+Solution

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

Example 4

~

+Checkpoint

+Checkpoint

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

Complete the following exercises

111

0

12

+SolutionCheckpoint