Parallel and Perpendicular Lines

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7-2
Parallel and Perpendicular Lines
Warm Up
Problem of the Day
Lesson Presentation
Course 3
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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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Problem of the Day The square root of
1,813,141,561 is a whole number. Is it odd or
even? How do you know?
Odd An odd number can only be the product of two
odd numbers.
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Learn to identify parallel and perpendicular
lines and the angles formed by a transversal.
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Insert Lesson Title Here
Vocabulary
parallel lines perpendicular lines transversal
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Parallel lines are lines in a plane that never
meet, like a set of perfectly straight, infinite
train tracks.
Perpendicular lines are lines that intersect at
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 two or
more lines that lie in the same plane.
Transversals to parallel lines form angles with
special 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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2
?1 _at_ ?3 _at_ ?5 _at_ ?7
3
4
?2 _at_ ?4 _at_ ?6 _at_ ?8
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6
7
8
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Check It Out Example 1
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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Check It Out 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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1
3
4
6
5
7
8
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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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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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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.
?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.
?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.
?6
m?6 56
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Check It Out Example 2A
In the figure, line n line m. Find the measure
of the angle.
All obtuse angles in the figure are congruent
?7
m?7 144
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Check It Out Example 2B
In the figure, line n line m. Find the measure
of the angle.
?5
?5 is supplementary to the angle 144.
m?5 144 180
m? 5 36
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Check It Out Example 2C
In the figure, line n line m. Find the measure
of the angle.
All acute angles in the figure are congruent
?1
m?1 36
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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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