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Geometry
Lesson 1 – 5
Angle Relationships
Objective:
Identify and use special pairs of angles.
Identify perpendicular lines.
Adjacent angles
2 angles that lie in the same plane and
have a common vertex and side, but no
common interior points.
Determine whether angles
1 and 2 are adjacent.
No, do not share
a common side
Yes
No, angles do not
share a vertex
or side.
Determine whether angles
1 and 2 are adjacent.
No, angles do
not share a side.
No, angles do not
share a vertex.
Determine whether angles
1 and 2 are adjacent.
No, angles do not
share a side.
Yes
No, angles do not
Share a vertex.
Determine whether the pair of
angles are adjacent.
A
AEC & CED
B
C
E
D
Yes
AEB & AEC
No, can’t have one angle
inside the other.
Linear Pair
A pair of adjacent angles with
noncommon sides that are opposite
rays.
Linear pairs are supplementary
Example
In the figure, CM and CE are opposite rays.
Name the angle that forms
a linear pair with angle 1
*Hint: what completes the
180 degrees or straight line
ACE
Do 3 & TCM form a linear pair?
Justify your answer.
No, they do not form a linear pair. The two angles
do not add up to be 180 and do not create opposite rays.
Your turn
Name the angle that forms
a linear pair with MCH
HCE
Tell whether TCE & TCM form a
linear pair. Justify your answer.
Yes, they are adjacent and their noncommon
sides are opposite rays.
Your Turn
Name the angle that forms
a linear pair with HCM
HCE
Do 1 & TCE
Justify your answer.
form a liner pair?
No, they are not adjacent angles.
Vertical Angles
Vertical angle:
 Two
angles are vertical if and only if
they are two nonadjacent angles
formed by a pair of interesting lines.
100
80
80
100
Theorem
Vertical angle Theorem:
 Vertical
angles are congruent.
Example
Find the value of x in each figure.
x = 130 (vertical)
5x = 25
x=5
Complementary Angles
2 angles with measures that have a
sum of 90.
Supplementary
Two angles with measures that have a
sum of 180.
Example
Find the measure of two supplementary
angles if the difference in the measures
of the two angles is 18.
Let one angle be x and the other y.
Write your equations.
x – y = 18
99 + y = 180
+
x + y = 180
2x = 198
x = 99
y = 81
Example
Find the measure of 2 complementary
angles if the measure of the larger
angle is 12 more than twice the
measure of the smaller angle.
Let x and y be the angles
x = 12 + 2y
x + y = 90
(12 + 2y) + y = 90
3y + 12 = 90
3y = 78
y = 26
x = 12 + 2(26)
= 64
Perpendicular Lines
Form 4 right angles
Form congruent adjacent angles
Segments and rays can be
perpendicular
Right angle symbol shows
perpendicular.
Example
Find x and y so that PR and SQ are
perpendicular.
2x + 5x + 6 = 90
7x + 6 = 90
7x = 84
x = 12
4y – 2 = 90
4y = 92
y = 23
Interpreting Diagrams
Are the lines perpendicular?
Interpret
What can you assume?
What appears true, but cannot be
assumed?
Determine whether each statement can be
assumed from the figure. Explain.
KHJ & GHM are complementary
No, congruent but we don’t know if complementary
GHK & JHK are a linear pair.
Yes, adjacent angles whose noncommon sides are opposite rays
HL  HM
Yes, they form a right angle which means they are perpendicular.
Homework
Pg. 50 1 – 7 all, 8 – 44 EOE,
58 – 66 E