Parallel and Perpendicular Lines

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Parallel and Perpendicular Lines

• 5.2

Pre-Algebra
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Warm Up
Complete each sentence. 1. Angles whose
measures have a sum of 90 are _______________ .
2. Vertical angles have equal measures, so they
are ______________. 3. Angles whose measures
have a sum of 180 are ______________. 4. A part
of a line between two points is called a
____________.
complementary
congruent
supplementary
segment
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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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Example 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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Example 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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2
?1 _at_ ? 3 _at_ ? 5 _at_ ? 7
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4
?2 _at_ ? 4 _at_ ? 6 _at_ ? 8
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6
7
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Try This
Measure the angles formed by the transversal and
parallel lines. Which angles seem to be congruent?
1
2
4
3
5
6
7
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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 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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1
3
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5
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PROPERTIES OF TRANSVERSALS TO PARALLEL LINES
If two parallel lines are intersected by a transversal, the acute angles that are formed are all congruent, the obtuse angles are all congruent, and any acute angle is supplementary to any obtuse angle. If the transversal is perpendicular to the parallel lines, all of the angles formed are congruent 90 angles.
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Example 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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Example 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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Example 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
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
In the figure, line n line m. Find the measure
of the angle.
B. ? 5
?5 is supplementary to the angle 144.
m? 2 144 180
m? 2 36
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Try This
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 36
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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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