1.5 complementary and supplementary angles
DESCRIPTION
Some slides lifted from: http://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=4&ved=0CEsQFjAD&url=http%3A%2F%2Fdionmath.wikispaces.com%2Ffile%2Fview%2F2.3%2BComplementary%2Band%2BSuppl.%2BAngles.ppt&ei=_wVFUbzHCa-o4AP9ooGwBQ&usg=AFQjCNF-KDyDx_yiVaUuMJMdM6yOJqHASQ&sig2=wH2TZ9xGxsHgtc4cCnn2QQ&bvm=bv.43828540,d.dmg&cad=rjaTRANSCRIPT
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WARM UP 1/22/13Mark no school on 1/20/13.
Identify the type of angle:
1.30°8. 60 °
2.120 ° 9. 158 °
3.180 ° 10. 80 °
4.90 °
5.72 °
6.140 °
7.116 °
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Complementary AnglesTwo angles are called complementary angles if the sum of their degree measurements equals 90 degrees.
Example:
These two angles are complementary. WHY????
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These two angles can be "pasted" together to form a right angle!
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Supplementary AnglesTwo angles are called supplementary angles if the sumof their degree measurements equals 180 degrees.
Example:
These two angles are supplementary. WHY???
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These two angles can be "pasted" together to form a straight line!
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Vertical AnglesPairs of Angle formed by the intersection of 2 lines.They are across from each other.
How many pairs?
Vertical angles are congruent!!!
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Review
State whether the following are acute, right, or obtuse.1.
2.
3.
4.
5.
??
acute obtuseright
obtuseacute
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Complementary and Supplementary
1. Two angles are complementary. One measures 65 degrees.
2. Two angles are supplementary. One measures 140 degrees.
Find the missing angle.
Answer : 25
Answer : 40
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Complementary and Supplementary
Find the missing angle. You do not have a protractor.Use the clues in the pictures.
1.2.x
55 165x
X=35 X=15
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Vertical Angles
Find the missing angle. You do not have a protractor.
Use the clues in the pictures.
58x
X=58
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Identify Complements and Supplements
• Determine whether the angles are complementary, supplementary, or neither.
a.
a. Because 22° + 158° = 180°, the angles are supplementary.
22° 158°
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• Determine whether the angles are complementary, supplementary, or neither.
b.
b. Because 15° + 85° = 100°, the angles are neither complementary or supplementary.
15° 85°
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• Determine whether the angles are complementary, supplementary, or neither.
c.
c. Because 55° + 35° = 90°, the angles are complementary.
35°55°
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Example Identify Complements and Supplements
Determine whether the angles are complementary, supplementary, or neither.
a. b. c.
SOLUTION
a. Because 22° + 158° = 180°, the angles are supplementary.
b. Because 15° + 85° = 100°, the angles are neither complementary nor supplementary.
c. Because 55° + 35° = 90°, the angles are complementary.
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Checkpoint Identify Complements and Supplements
ANSWER supplementary
ANSWER complementary
Determine whether the angles are complementary, supplementary, or neither.
1. ANSWER neither
2.
3.
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• Tell whether the numbered angles are adjacent or nonadjacent.
a.
a. Because the angles do not share a common vertex or a common side, then
and are nonadjacent.
1
2
21
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• Tell whether the numbered angles are adjacent or nonadjacent.
b.
Because the angles share a common vertex and a common side, and they do not have an common interior points, and
are adjacent.
3 4
43
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• Tell whether the numbered angles are adjacent or nonadjacent.
c.
Although and share a common vertex, they do not share a common side. Therefore, andare nonadjacent.
5
6
655 6
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Example Measures of Complements and Supplements
A is a complement of C, and mA = 47°. Find mC.a.
b. P is a supplement of R, and mR = 36°. Find mP.
SOLUTION
a. A and C are complements, so their sum is 90°.
b.P and R are supplements, so their sum is 180°.
mA + mC = 90° mP + mR = 180°
47° + mC = 90° mP + 36° = 180°
47°+ mC – 47° = 90° – 47° mP + 36° – 36° = 180° – 36°
mC = 43° mP = 144°
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Checkpoint Measures of Complements and Supplements
B is a complement of D, and mD = 79°. Find mB.4.
5. G is a supplement of H, and mG = 115°. Find mH.
ANSWER 11°
ANSWER 65°
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Congruent Complements Theorem
1 12 3
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Congruent Supplements Theorem
1 12 3
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SOLUTION
7 and 9 are both supplementary to 8. So, by the Congruent supplements Theorem, 7 9.
7 and 8 are supplementary, and 8 and 9 are supplementary. Name a pair of congruent angles. Explain your reasoning.
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ANSWER10 12; 10 and 12 are both complementary to 11, so 10 12 by the Congruent Complements Theorem.
In the diagram, m10 + m11 = 90°, and m11 + m12 = 90°.
Name a pair of congruent angles. Explain your reasoning.
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More drawings
20
C
J
D
E F
G
H
70
9070
20
90
I
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Final Drawing
52
B
A
F E
D
C
60
G
68
686052