Transcript Introduction to Proof: Part I Types of Angles

Introduction to Proof:
During this lesson, we will:
 Identify angles as adjacent or vertical
 Identify supplementary and
complementary angles and find their
measures
Mrs. McConaughy
Geometry
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Introduction to Proof: Part
I Types of Angles
Mrs. McConaughy
Geometry
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Review: Classifying Angles By
Their Measures
Recall, the degree measure, m, of an
angle must be 0 > m ≥ 180.
Angles can be classified into four
categories by their measures:
Acute Obtuse Right Straight
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Classifying Angles By Their Position
With Respect to Each Other
two coplanar angles
Adjacent angles :_________________
______________________________
with a common side, a common vertex,
and no common interior points
______________________________
Which angles are adjacent to one another?
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Classifying Angles By Their Position
With Respect to Each Other
nonadjacent angles
Vertical angles: _________________
formed by intersecting lines. Vertical
______________________________
angles share a common vertex and
______________________________
have sides which are opposite rays.
______________________________
Which angles form vertical angle pairs?
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Introduction to Proof: Part
II Complementary &
Supplementary Angles
During this lesson, you will:
identify supplementary and complementary
angles
determine the measures of supplementary
and complementary angles
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Definitions: Supplementary
Angles and Linear Pairs
Two angles are supplementary if the
sum of their measures is 180 degrees.
Each angle is called a supplement of the
other.
If the angles are adjacent and
supplementary, they are called a linear
pair.
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
Alert!Supplementary
Supplementary angles
do not have
to be
Angles
and
adjacent. If they are adjacent, then the sides
Linear
Pairs
of the two angles whichm<
are
not
PQS
+ mthe
<SQRcommon
= 180
< PQS and < SQR are a linear pair
side form a straight angle.
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2
m < 1 + m < 2 = 180
< 1 supplements < 2
< 1 is a supplement of < 2
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m< GHJ + m <JHI = 180
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< GHJ
and < JHI are a linear pair
Example 1
Which are measures of
supplementary angles?
30 ° and 160°
103° and 67°
86° and 94°
86° and 94°
180
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Definition: Complementary
Angles
Complementary angles are related to right
angles.
Definition:
Complementary
Angles
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Two angles are
complementary if the sum of
their measures is 90
degrees. Each angle is
called a complement of the
other.
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Complementary angles do not have to be adjacent.
Complementary
Angles
If they
are adjacent, then the sides
of the two
angles which are not the common side form a right
angle.
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Example 2
Find the measure of a complement of
each angle, if possible. Find the
measure of a supplement.
Angle
Measure
Complement
90
Supplement
180
90 - m
180 - m
??
60°
95°
m°
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Example 3
Find the measure of an angle if its
measure is 60° more than its supplement.
m = 180 – m + 60
Alert! We will use the m, 90 - m, and 180 – m to solve
problems about angles.
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Example 4
Find the measure of an angle if its
measure is twice that of its supplement.
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Example 5
Find the measure of an angle if its measure is
40 less than four times the measure of its
complement.
measure is 40 less than four times the measure of its complement.
m = 4 (90 – m) -
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40
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Final Checks for Understanding
Which are measures of complementary
angles?…supplementary angles?
...neither?
1. 60° & 30°
2. 130° & 50°
3. 114° & 66°
4. 92° & 2°
5. 53° & 47°
6. 87° & 87°
7. 45° & 45°
8. 26° & 154°
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Final Checks for Understanding
What is the measure of a complement of
each angle whose measure is given?
1. 45°
2. 20°
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3. 78°
4. 46°
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22.5
6. (m-5)°
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Final Checks for Understanding
Translate words
mathematical symbols
Complementary
Supplementary
___________________ __________________
“a more than b”
_______________________
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“a less than b”
_______________________
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Homework
Complementary &
Supplementary Angles
WS
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