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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