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Applied Geometry
Lesson 3 – 4
Adjacent Angles and Linear
Pairs of Angles
Objective:
Learn to identify and use adjacent angles and linear pairs of angles.
Adjacent Angles
Adjacent angles:

Angles that share a common side and
have the same vertex, but have no interior
points in common.
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
Linear Pair:
 Two
angles form a linear pair if and
only if they are adjacent and their
noncommon sides are opposite rays.
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.
Real world problem
The John Hancock Center in
Chicago, Illinois, contains
many types of angles.
Describe
the highlighted angles.
The angles are adjacent and
form a linear pair.
Real World
Name examples of linear pairs in real
world. (classroom etc.)
Homework
Pg. 112 1 – 7 all, 8 – 26 E