Warm Up

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Preview
Warm Up
California Standards
Lesson Presentation
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Warm Up Classify each angle with the given
measure as acute, right, obtuse, or
straight. 1. 125 2. 90 3. 85 4. 180
right
obtuse
acute
straight
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Objective You will learn how to (YWLHT)
identify and describe angle pairs.
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Vocabulary
vertical angles adjacent angles complementary
angles supplementary angles
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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.
?NRQ and ?QRP are adjacent angles. They share
vertex R and RQ.
?MRN and ?NRQ are adjacent angles. They share
vertex R and RN.
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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.
?MRN and ?PRQ are vertical angles.
?MRP and ?NRQ are vertical angles.
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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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Example 2 Identifying Adjacent and Vertical
Angles Tell whether the numbered angles are
adjacent or vertical. B.
?7 and ?8 are side by side and have a common
vertex and ray.
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They are adjacent angles.
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Check It Out! Example 3 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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Check It Out! Example 4 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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Complementary angles are two angles whose
measures have a sum of 90.
?LMN and ?NMP are complementary.
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Supplementary angles are two angles whose
measures have a sum of 180.
?GFE and ?HJK are supplementary.
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Example 5 Identifying Complementary and
Supplementary Angles
Use the diagram to tell whether the angles are
complementary, supplementary, or neither.
A. ?OMP and ?PMQ
Since 60 30 90, ?PMQ and ?OMP are
complementary.
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Example 6 Identifying Complementary and
Supplementary Angles
Use the diagram to tell whether the angles are
complementary, supplementary, or neither.
B. ?NMO and ?OMR
Since 15 165 180, ?NMO and ?OMR are
supplementary.
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Example 7 Identifying Complementary and
Supplementary Angles
Use the diagram to tell whether the angles are
complementary, supplementary, or neither.
C. ?PMQ and ?QMR
Since 30 75 105, ?PMQ and ?QMR are neither
complementary nor supplementary.
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Check It Out! Example 8
Use the diagram to tell whether the angles are
complementary, supplementary, or neither.
A. ?BAC and ?CAF
Since 35 145 180, ?BAC and ?CAF are
supplementary.
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Check It Out! Example 9
Use the diagram to tell whether the angles are
complementary, supplementary, or neither.
B. ?CAD and ?EAF
D
E
C
B
F
A
Since 55 35 90, ?CAD and ?EAF are
complementary.
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Check It Out! Example 10
Use the diagram to tell whether the angles are
complementary, supplementary, or neither.
C. ?BAC and ?EAF
Since 35 35 70, ?BAC and ?EAF are neither
supplementary nor complementary.
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Home Learning
On-Line Tutoring
Geo-match-try
Geo-fit
Geo-Terms
Geo-Vocab
Shape Quiz
Angle Tangle
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Lesson Quiz
1. Tell whether the numbered angles are vertical
or adjacent.
adjacent
Use the diagram to tell whether the angles are
complementary, supplementary, or neither.
2. ?AZB and ?BZC 3. ?BZC and ?CZD
neither
complementary