Download 1‐5: Exploring Angle Pairs Types of Angle Pairs •

1‐5:ExploringAngle
Pairs
TypesofAnglePairs
• Adjacent Angles
Two coplanar angles with a: common side common vertex
_______________, ________________, _______________________________
no common interior points
1
2
3
4
• Vertical Angles
Two angles whose sides are __________ ______
opposite rays
1
3
2
4
B
• Complementary Angles
Two angles whose measures have a sum of _______
90
47 
43 
1
2
A
• Supplementary Angles
Two angles whose measures have a sum 180
of _______
3
4
1
Example1:Usethediagrambelow.Iseachstatementtrue?Explain.
L
M
P
A
74 
106
O
N
a. PAL and are adjacent angles.
LAM
Yes, they have a common side
NAM
b. PAO and are vertical angles.
No, they don’t share two pairs of opposite rays
NAO
c. PAO and are supplementary.
Yes, the sum of the angles is 180°
AssumptionsAboutAngles
• Assumptions you can make:
1. Angles are adjacent
2. Angles are adjacent and supplementary
3. Angles are vertical angles
• Assumptions you can’t make:
1. Angles or segments are congruent
2. An angle is a right angle
3. Angles are complementary
2
Postulate1‐9:LinearPairPostulate
A Linear Pair of angles are angles that are both supplementary and adjacent.
ABC
DBC
Ex 2 What are the measures of and ?
C
3 x  19
3x  19  7 x  9  180
10 x  10  180
10 x  170
x  17
A
7x  9
B
D
mABC  3(17)  19  70
mDBC  7(17)  9  110
Theorem2‐1:VerticalAngleTheorem
Vertical angles are congruent
1  3 and 2  4
1
2
4
3
Example 3: What is the value of x? What are the angle measures?
2 x  42  3 x  10
2 x  52  3 x
52  x
(2 x  42)
(3x  10)
2(52)  42  146
3(52)  10  146
3
AngleBisector
two
• A ________ which divides an angle into ______ ray
_______________ angles.
congruent
X

AY is an angle bisector.
A
Y
Z

JLN mJLM  42
LM
Example 4: bisects . If , what is
mJLN ?
J
2(42)  84
42
L
M
N
Homework:p.38#7‐23,27‐32
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