Transcript Slide 1

9-3 Angle Relationships
California
Standards
MG2.1 Identify angles as vertical,
adjacent, complementary, or
supplementary and provide descriptions
of these terms.
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9-3 Angle Relationships
Vocabulary
vertical angles
adjacent angles
complementary angles
supplementary angles
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9-3 Angle Relationships
Angles are congruent if they have the same
measure.
Adjacent angles are two angles that are side
by side and have a common vertex and ray.
Adjacent angles may or may not be congruent.
MRN and NRQ are adjacent angles. They
share vertex R and RN.
NRQ and QRP are adjacent angles. They
share vertex R and RQ.
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9-3 Angle Relationships
Vertical angles are two angles that are formed
by two intersecting lines and are not adjacent.
Vertical angles have the same measure, so they
are always congruent.
MRP and NRQ are vertical angles.
MRN and PRQ are vertical angles.
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9-3 Angle Relationships
Additional Example 1: Identifying Adjacent
and Vertical Angles
Tell whether the numbered angles are
adjacent or vertical.
A.
5
6
5 and 6 are opposite each other and
are formed by two intersecting lines.
They are vertical angles.
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9-3 Angle Relationships
Additional Example 1: Identifying Adjacent
and Vertical Angles
Tell whether the numbered angles are
adjacent or vertical.
B.
7
8
7 and 8 are side by side and
have a common vertex and
ray.
They are adjacent angles.
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9-3 Angle Relationships
Check It Out! Example 1
Tell whether the numbered angles are
adjacent or vertical.
A.
3 and 4 are side by side and
have a common vertex and
ray.
3
4
They are adjacent angles.
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9-3 Angle Relationships
Check It Out! Example 1
Tell whether the numbered angles are
adjacent or vertical.
B.
7
8
7 and 8 are opposite each other and
are formed by two intersecting lines.
They are vertical angles.
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9-3 Angle Relationships
Complementary angles are two angles
whose measures have a sum of 90°.
65° + 25° = 90°
LMN and NMP are complementary.
L
N
65°
25°
M
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P
9-3 Angle Relationships
Supplementary angles are two angles whose
measures have a sum of 180°.
65° + 115° = 180°
GFE and HJK are supplementary.
E
H
65°
G
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115°
F
J
K
9-3 Angle Relationships
Additional Example 2: Identifying Complementary
and Supplementary Angles
Use the diagram to tell whether the angles are
complementary, supplementary, or neither.
A. OMP and PMQ
To find mPMQ, start with the measure that QM
crosses, 105°, and subtract the measure that MP
crosses, 75°. mPMQ = 105° – 75° = 30°.
P
Q
mOMP = 75° – 15° = 60°.
Since 60° + 30° = 90°,
PMQ and OMP are
complementary.
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O
N
M
R
9-3 Angle Relationships
Reading Math
If the angle you are measuring
appears obtuse, then its measure is
greater than 90°. If the angle you are
measuring is acute, its measure is
less than 90°.
Holt CA Course 1
9-3 Angle Relationships
Additional Example 2: Identifying Complementary
and Supplementary Angles
Use the diagram to tell whether the angles are
complementary, supplementary, or neither.
B. NMO and OMR
mNMO = 15° and mOMR = 165°
P
Since 15° + 165° = 180°,
NMO and OMR are
supplementary.
Q
O
N
M
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R
9-3 Angle Relationships
Additional Example 2: Identifying Complementary
and Supplementary Angles
Use the diagram to tell whether the angles are
complementary, supplementary, or neither.
C. PMQ and QMR
To find mPMQ, start with the measure that QM
crosses, 105°, and subtract the measure that MP
crosses, 75°. mPMQ = 105° – 75° = 30°.
mQMR = 75°.
P
Q
Since 30° + 75° = 105°,
PMQ and QMR are
neither complementary
nor supplementary.
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O
N
M
R
9-3 Angle Relationships
Check It Out! Example 2
Use the diagram to tell whether the angles are
complementary, supplementary, or neither.
A. BAC and CAF
mBAC = 35° and mCAF = 145°
Since 35° + 145° = 180°,
BAC and CAF are
supplementary.
D
E
C
F
B
A
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9-3 Angle Relationships
Check It Out! Example 2
Use the diagram to tell whether the angles are
complementary, supplementary, or neither.
B. CAD and EAF
To find mCAD, start with the measure that DA
crosses, 90°, and subtract the measure that CA
crosses, 35°. mCAD = 90° – 35° = 55°.
mEAF = 35°.
D
Since 55° + 35° = 90°,
CAD and EAF are
complementary.
E
C
B
F
A
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9-3 Angle Relationships
Check It Out! Example 2
Use the diagram to tell whether the angles are
complementary, supplementary, or neither.
C. BAC and EAF
mBAC = 35° and mEAF = 35°
Since 35° + 35° = 70°,
BAC and EAF are
neither supplementary
C
nor complementary.
D
E
F
B
A
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