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Lesson 4: Exploring Angle Pairs
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A
B
C
D
M
P
ON
adjacent angles: two angles with 1) a common side, 2) a common vertex, and 3) no common interior points
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linear pair: adjacent angles whose noncommon sides form opposite rays (they make a straight line!)
1 2
example: <1 & <2 are a linear pair
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vertical angles: two angles that have sides forming two pairs of opposite rays (they make an x!)
123
4
example:<1 & <3 are vertical angles<2 & <4 are vertical angles
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a) Are <1 & <2 a linear pair?b) Are <4 & <5 a linear pair?c) Are <5 & <3 vertical angles?d) Are <1 & <3 vertical angles?e) Are <5 & <3 adjacent angles?
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supplementary angles: two angles whose sum is 180o
Given that <G is a supplement of <H and m<G is 82o, find m<H.
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complementary angles: two angles whose sum is 90o
Given that <G is a complement of <H and m<G is 82o, find m<H.
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Name an angle that is supplementary to <ABE.
Name an angle that is complementary to <EBF.
A B C
DE
F
60o 60o
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IMPORTANT:A linear pair is supplementary.
They add up to 180o!
123
4m< + m< = 180o
m< + m< = 180o
m< + m< = 180o
m< + m< = 180o
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IMPORTANT:Vertical angles are congruent.
They have the same measure.
123
4< <
< <
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1. What are the relationships between <DGE & <FGE?
2. Find m<CGF.
3. Find m<CGD.
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Solve for x and y. Then find the angle measures.
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A
X
Z
YAY XAZis a bisector for
angle bisector: a ray that divides an angle into two congruent parts
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Classwork/Homework
Pg. 38 #7 26