Learn to identify parallel and perpendicular lines and the angles formed by a transversal'

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Learn to identify parallel and perpendicular
lines and the angles formed by a transversal.
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Vocabulary
parallel lines perpendicular lines transversal
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Parallel lines are two lines in a plane that
never meet, like a set of perfectly straight,
infinite train tracks.
Perpendicular lines are lines that intersect to
form 90 angles.
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The railroad ties are transversals to the tracks.
The tracks are parallel.
A transversal is a line that intersects any two
or more other lines. Transversals to parallel
lines have interesting properties.
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Additional Example 1 Identifying Congruent
Angles Formed by a Transversal
Measure the angles formed by the transversal and
parallel lines. Which angles seem to be congruent?
?1, ? 3, ? 5, and ? 7 all measure 150.
? 2, ? 4, ? 6, and ? 8 all measure 30.
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Additional Example 1 Continued
Angles marked in blue appear to be congruent to
each other, and angles marked in red appear to be
congruent to each other.
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?1 _at_ ? 3 _at_ ? 5 _at_ ? 7
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?2 _at_ ? 4 _at_ ? 6 _at_ ? 8
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Try This 1 Example 1
Measure the angles formed by the transversal and
parallel lines. Which angles seem to be congruent?
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4
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5
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?1, ? 4, ? 5, and ? 8 all measure 36.
? 2, ? 3, ? 6, and ? 7 all measure 144.
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Try This 1 Example 1 Continued
Angles marked in blue appear to be congruent to
each other, and angles marked in red appear to be
congruent to each other.
?1 _at_ ? 4 _at_ ? 5 _at_ ? 8
?2 _at_ ? 3 _at_ ? 6 _at_ ? 7
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Additional Example 2A Finding Angle Measures of
Parallel Lines Cut by Transversals
In the figure, line l line m. Find the measure
of the angle.
All obtuse angles in the figure are congruent.
A. ?4
m? 4 124
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Additional Example 2B Finding Angle Measures of
Parallel Lines Cut by Transversals Continued
In the figure, line l line m. Find the measure
of the angle.
B. ? 2
?2 is supplementary to the angle 124.
m?2 124 180
m? 2 56
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Additional Example 2C Finding Angle Measures of
Parallel Lines Cut by Transversals Continued
In the figure, line l line m. Find the measure
of the angle.
All acute angles in the figure are congruent.
C. ? 6
m? 6 56
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Try This Example 2A
In the figure, line n line m. Find the measure
of the angle.
All obtuse angles in the figure are congruent
A. ? 7
m? 7 144
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Try This Example 2B
In the figure, line n line m. Find the measure
of the angle.
B. ? 5
?5 is supplementary to the angle 144.
m? 5 144 180
m? 5 36
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Try This Example 2C
In the figure, line n line m. Find the measure
of the angle.
All acute angles in the figure are congruent
C. ? 6
m? 6 144
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If two lines are intersected by a transversal and
any of the angle pairs shown below are congruent,
then the lines are parallel. This fact is used in
the construction of parallel lines.
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Lesson Quiz
In the figure a b.
1. Name the angles congruent to ?3.
?1, ?5, ?7
2. Name all the angles supplementary to ?6.
?1, ?3, ?5, ?7
3. If m?1 105 what is m?3?
105
4. If m?5 120 what is m?2?
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