Transcript 1.5 Exploring Angle Pairs 9/20/10 • Types of Angle Pairs – Adjacent Angles – Vertical Angles – Complementary Angles – Supplementary Angles.

1.5 Exploring Angle Pairs 9/20/10
• Types of Angle Pairs
– Adjacent Angles
– Vertical Angles
– Complementary Angles
– Supplementary Angles
Adjacent Angles
• Adjacent angles – two coplanar angles with a
common side, a common vertex, and no
common interior points.
1and 2
3and 4
Vertical Angles
• Vertical angles – two angles whose sides are
opposite rays.
1and 2
3and 4
Complementary Angles
• Complementary angles – two angles whose
measures have a sum of 90°.
– Each angle is called the complement of the other.
1and 2
Aand B
Supplementary Angles
• Supplementary angles – two angles whose
measures have a sum of 180°.
– Each angle is called the supplement of the other.
3and 4
Band C
Identifying Angle Pairs
• Use the diagram. Is the statement true? Explain.
a. BFDand CFD are adjacent angles.
b. AFBand EFD are vertical angles.
c. AFEand BFC are complementary.
Identifying Angle Pairs
a. No, they are not adjacent. They have a
common side and common vertex, but they
also have common interior points.
b. No, they are not vertical angles. Ray FA and
ray FD are opposite rays, but ray FE and ray
FB are not.
c. Yes, they are complementary. 62 + 28 = 90°.
Linear Pairs
• A linear pair is a pair of adjacent angles whose
noncommon sides are opposite rays.
– The angles of a linear pair form a straight angle.
• Postulate 1.9 Linear Pair Postulate
– If two angles form a linear pair, then they are
supplementary.
Finding Missing Angle Measures
KPLand JPL are a linear pair.
mKPL  2 x  24, andmJPL  4 x  36.
What are the measures of
KPLand JPL?
Finding Missing Angle Measures
mKPL  mJPL  180
(2 x  24)  (4 x  36)  180
6 x  60  180
6 x  120
x  20
mKPL  2x  24  2(20)  24  40  24  64
mJPL  4 x  36  4(20)  36  80  36  116
Angle Bisector
• An angle bisector is a ray that divides an angle into
two congruent angles.
– Its endpoint is at the angle vertex.
– Within the ray, a segment with the same endpoint is also
an angle bisector.
• The ray or segment bisects the angle.
Using an Angle Bisector to Find Angle Measures
•
ACbisects
what is
. If
DAB
mDAC ?
,  58
mDAB
mCAB  mDAC
 58
mDAB  mCAB  mDAC
 58  58
 116
More Practice!!!!!
• Classwork – Textbook p. 38 # 7 – 25 odd.
• Homework – Textbook p. 38 # 8 – 26 even.