Download Section 1.5: Exploring Angle Pairs

September 05, 2014
Section 1.5: Exploring Angle Pairs
Objective: To identify special angle pairs and use their relationships
to find angle measures
a pair of adjacent angles whose noncommon sides are
opposite rays (form a straight angle)
a ray that divides an angle into two congruent angles
(endpoint is at the vertex)
2 angles with a
common side, a
common vertex,
and no common
interior points
two angles whose two angles whose two angles whose
sides are opposite measures have a measures have a
sum of 90
sum of 180
rays
m_1 + m_2 = 180
1
2
September 05, 2014
Date:
Section 1.5: Exploring Angle Pairs
Objective: To identify special angle pairs and use their relationships
to find angle measures
Example 1: Identifying Angle Pairs
Decide if each statement is true. Explain.
a. _
_PAL and _
_LAM are adjacent angles.
b. _
_PAO and _
_NAM are vertical angles.
L
P
A
74o
O
c. _
_PAO and _
_NAO are supplementary.
M
106o
N
September 05, 2014
Section 1.5: Exploring Angle Pairs
Objective: To identify special angle pairs and use their relationships
to find angle measures
Example 2: Find Missing Angle Measurements
What can you conclude from the information in the diagram?
Congruent Angles:
Linear Pairs:
5
4
Vertical Angles:
3
Adjacent Angles:
Quick Check: Can you make each conclusion? Explain.
a. TW
WV
c. _TWQ is a right angle.
b. PW
WQ
d. TV bisects PQ
1
2
September 05, 2014
Section 1.5: Exploring Angle Pairs
Objective: To identify special angle pairs and use their relationships
to find angle measures
Example 3: Finding Missing Angle Measures
_
_
_ABC and _
_DBC are a linear pair. m_ABC
= 3x+19, and m_DBC
= 7x-9.
_
What are the measures of _
_ABC and _
_DBC?
_ADB and _
_BDC are a linear pair. m_ADB
= 3x+14 and
_
Quick Check: _
_
_
m_BDC
= 5x-2. What are m_ADB
and m_BDC?
_
September 05, 2014
Section 1.5: Exploring Angle Pairs
Objective: To identify special angle pairs and use their relationships
to find angle measures
Example 4: Using and Angle Bisector to Find Angle Measures
_
_
LM bisects _
_JLN. If m_JLM
= 42o, what is m_JLN?
_
Quick Check: KM bisects _
_JKL. If m_JKL
= 72o, what is m_JKM?
_
September 05, 2014
Homework:
P. 38 #7-28
*Bring a compass to
class on Monday*