Angle Relationship
Sec 1.5
Sol: G.3 and G.11
Adjacent Angles
Definition: 2 angles that lie on the same plane,
have a common vertex and a common side,
but have no common interior points.
Example:
A
Non – Example:
D
C
C
B
B
D
ABCandCBD
A
ABCandBCD
No Common Vertex
Vertical Angles
Definition: 2 non-adjacent angles formed by two intersecting
lines. Opposite angles are congruent.
Lesson 1-5: Pairs of Angles
Examples:
A
1 and 3
1
4
2 and 4
D
B
Q
2
3
C
Vertical Angles Cont.
Non – Example:
Remember: To form a vertical pair you have to
have two intersection lines.
Linear Pair
Definition: Is a pair of adjacent angles who’s
non-common sides are opposite rays.
Example:
A
BDA and CDA are
a linear pair
B
Non-example:
D
C
EX: Identify angle pairs
1
1. Identify the vertical pairs.
2. Identify all the linear pairs.
3. Identify the Adjacent angles.
2 3
4
5
Complementary Angles
Definition: A pair of angles whose sum is 90˚
m2 = 50°
Examples:
A
B
2
Q
A
B
F
2
1
Q
C
m1  m2  90
m1 = 40°
1
R
G
Even when two angles are
non adjacent they can be
Added together to form a 90 degree angles
Lesson 1-5: Pairs of Angles
9
Supplementary Angles
Definition: A pair of angles whose sum is 180˚
Examples:
B
Adjacent supplementary angles are
also called “Linear Pair.”
2
1
Q
A
C
B
F
Non-Adjacent Angles
2
m1 = 40°
m2 = 140°
A
1
Q
R
Lesson 1-5: Pairs of Angles
G
10
Ex: Angle Measure
Find the measure of two Complimentary angle if
m1 = 2x + 3 and m2 = 3x – 8.
Perpendicular Lines
Definitions: Lines that form two right angles.
Can intersect to form 4 right angles
Intersect to form congruent adjacent angles.
Segments and rays can be perpendicular to
lines or other segments and rays.
When you see a right angle symbol it
represents perpendicular lines.
Symbolized By :  Read “Perpendicular to”
Example
X
Y
XZ  YW
Z
W
Example:
Find x and y so that BEand AD are
Perpendicular