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Pairs of
Angles
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Adjacent Angles
Definition: A pair of angles with a shared vertex and common
side but do not have overlapping interiors.
Examples: 1 and 2 are adjacent. 3 and 4 are not.
1 and ADC are not adjacent.
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Adjacent Angles( a common side )
Non-Adjacent Angles
2
Complementary Angles
Definition: A pair of angles whose sum is 90˚
Examples:
Adjacent Angles
( a common side )
Non-Adjacent Angles
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Supplementary Angles
Definition: A pair of angles whose sum is 180˚
Examples:
Adjacent supplementary angles are
also called “Linear Pair.”
Non-Adjacent Angles
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Vertical Angles
Definition: A pair of angles whose sides form opposite rays.
Examples:
Ð1 and Ð3
Ð2 and Ð4
Vertical angles are non-adjacent angles formed by intersecting
lines.
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Theorem: Vertical Angles are ~
=
Given:
The diagram
Prove:
Ð1 @ Ð3
Statements
Reasons
1.
1. Definition: Linear Pair
2. mÐ1 + mÐ2 = mÐ2 + mÐ3
2. Property: Substitution
3. mÐ1 = mÐ3
3. Property: Subtraction
4. mÐ1 @ mÐ3
4. Definition: Congruence
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What’s “Important” in Geometry?
4 things to always look for !
360˚
. . . and
Congruence
180˚
90˚
Most of the rules (theorems)
and vocabulary of Geometry
are based on these 4 things.
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Example: If m4 = 67º, find the measures
of all other angles.
Step 1: Mark the figure with given info.
Step 2: Write an equation.
m3  m4  180
m3  67 180
67º
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4
2
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m3 180  67  113
Because 4 and 2 arevertical angles, they are equal. m4  m2  67
Because 3 and 1 are vertical angles, they are equal. m3  m1  117
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Example: If m1 = 23 º and m2 = 32 º, find the
measures of all other angles.
Answers:
m4  23 (1 & 4 are vertical angles.)
m5  32 (2 & 5 are vertical angles.)
m1  m2  m3  180
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23  32  m3  180
m3  180  55  125
m3  m6  125
3 & 6 are vertical angles.
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3
6
4
5
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Example: If m1 = 44º, m7 = 65º find the
measures of all other angles.
Answers: m3  90
m1  m4  44
m4  m5  90
44  m5  90
m5  46
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5
6
3
2
1
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m6  m7  90
m6  65  90
m6  25
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