Download 1-5: Exploring Angle Pairs

1-5: Exploring Angle
Pairs
Types of Angle Pairs
• 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
90
of _______
47 
1
2
A
• Supplementary Angles
Two angles whose measures have a sum
180
of _______
3
4
43 
Example 1: Use the diagram below. Is each statement true? Explain.
L
M
P
74 
A
106
O
N
a. PAL and LAM are adjacent angles.
Yes, they have a common side
b. PAO and NAM are vertical angles.
No, they don’t share two pairs of opposite rays
c. PAO and NAO are supplementary.
Yes, the sum of the angles is 180°
Assumptions About Angles
• 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
Postulate 1-9: Linear Pair Postulate
A Linear Pair of angles are angles that are
both supplementary and adjacent.
Ex 2 What are the measures of ABC and DBC ?
C
3 x  19  7 x  9  180
10 x  10  180
10 x  170
x  17
3 x  19
A
7x  9
B
D
mABC  3(17)  19  70
mDBC  7(17)  9  110
Theorem 2-1: Vertical Angle Theorem
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  42)
(3 x  10)
2 x  52  3 x
52  x
2(52)  42  146
3(52)  10  146
Angle Bisector
two
• A ________
which divides an angle into ______
ray
_______________
angles.
congruent
X
AY is an angle bisector.
A
Y
Z
Example 4: LM bisects JLN . If mJLM  42, what is
mJLN ?
J
2(42)  84
42
L
M
N
Homework: p. 38 # 7-23, 27-32