Warm Up

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• Warm Up
• Identify each of the following.
• 1. points that lie in the same plane
• 2. two angles whose sum is 180
• 3. the intersection of two distinct intersecting
  lines
• 4. a pair of adjacent angles whose non-common
  sides are opposite rays

coplanar points
supplementary angles
point
linear pair
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Objectives
Identify parallel, perpendicular, and skew lines.
Identify the angles formed by two lines and a
transversal.
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Example 1 Identifying Types of Lines and Planes
Identify each of the following.
A. a pair of parallel segments
B. a pair of skew segments
C. a pair of perpendicular segments
D. a pair of parallel planes
plane NMR plane KLQ
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Check It Out! Example 1
Identify each of the following.
a. a pair of parallel segments
b. a pair of skew segments
c. a pair of perpendicular segments
d. a pair of parallel planes
plane FJH plane BCD
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Example 2 Classifying Pairs of Angles
Give an example of each angle pair.
A. corresponding angles
?1 and ?5
B. alternate interior angles
?3 and ?5
C. alternate exterior angles
?1 and ?7
D. same-side interior angles
?3 and ?6
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Check It Out! Example 2
Give an example of each angle pair.
A. corresponding angles
?1 and ?3
B. alternate interior angles
?2 and ?7
C. alternate exterior angles
?1 and ?8
D. same-side interior angles
?2 and ?3
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Example 3 Identifying Angle Pairs and
Transversals
Identify the transversal and classify each angle
pair.
A. ?1 and ?3
transversal l corr. ?s
B. ?2 and ?6
transversal n alt. int ?s
C. ?4 and ?6
transversal m alt. ext ?s
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Objective
Students will Use the angles formed by a
transversal to prove two lines are parallel.
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Remember! Converse of a theorem is found by
exchanging the hypothesis and conclusion. The
converse of a theorem is not automatically true.
If it is true, it must be stated as a postulate
or proved as a separate theorem.
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Use the given information and the theorems you
have learned to show that r s.
?4 ? ?8
?4 ? ?8 ?4 and ?8 are alternate exterior angles.
r s Conv. Of Alt. Ext. ?s Thm.
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Use the given information and the postulates you
have learned to show that l m.
?1 ? ?3 ?1 and ?3 are
corresponding angles.
l m Conv. of Corr. ?s Post.
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Which postulate proves that l m? m?3 (4x
80), m?7 (3x 50), x 30
m?3 4(30) 80 40 Substitute 30 for x.
m?7 3(30) 50 40 Substitute 30 for x.
m?3 m?7
?3 ? ?7 Def. of ? ?s.
l m Conv. of Corr. ?s Post.
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