3.1: Parallel Lines and
Transversals
Chapter 3: Angles and Triangles
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What is a Transversal?
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Lines in the same plant that do not
intersect are called parallel lines.
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Lines that intersect at rights angles
are called perpendicular lines.
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Transversal- a line that intersects
two or more lines.
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When parallel lines are cut by a
transversal, several pairs of
congruent angles are formed.
Corresponding Angles
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When a transversal intersects
parallel lines, corresponding
angles are congruent.
Finding Angle Measures
Use the figure to find the measures of (a) <1 and (b) <2.
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(a) <1 and the 110 degree angles
are corresponding angles. They
are congruent
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<1 and <2 are supplementary,
The sum of the angles is 180
degrees.
 1  2  1800
1100   2  1800
 2  700
Practice
Use the figure to find the measure of <1 and <2. explain your reasoning.
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<1 and 63 degrees are
corresponding angles, sot <1 is
63 degrees.
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<1 and <2 are supplementary
angles.
 1  2  180 0
63 0   2  180 0
 2  117 0
Using Corresponding Angles
Use the figure to find the measures of the numbered angles.
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<1 and the 75 degree angle are
vertical angles, so they are
congruent.
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The 75 degree angle is supplementary
to both <2 and <3.
750   2  1800
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 2  1050
So, the measures of <2 and <3 are
105
Using corresponding angles, the measures
 of <4 and<6 are 75, and the
measures of <5 and <7 are 105.
Practice
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Use the figure to find the
measure of the numbered angles.
 1  1210
 2  590
 3  1210
 4  1210
 5  590
 6  1210
 7  590
Interior and Exterior Angles
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When two parallel lines are cut by
a transversal:
S Four interior angles are
formed on the inside of the
parallel lines.
S Four exterior angles are
formed on the outside of the
parallel lines.
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<3, <4, <5, and <6 are interior
angles.
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<1, <2, <7, and <8 are exterior
angles.
Using Corresponding Angles
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A store owner uses pieces of tape
to paint a window advertisement.
The letters are slanted at an 80
degree angle. What is the
measure of <1?
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Because all the letters are slanted at an
80 degree angle, the dashed lines are
parallel. The pieces of tape is the
transversal.
S Using corresponding angles, the 80
degree angle is congruent to the
angle that is supplementary to <1.
The measure of <1 is 180-80=100 degrees.
Alternate Interior and Alternate
Exterior Angles
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When a transversal intersects
parallel lines
S Alternate interior angles are
congruent
S Alternate exterior angles are
congruent
Identifying Alternate Interior
and Alternate Exterior Angles
The photo shows a portion of an airport. Describe the relationship
between each pair of angles.
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<3 and <6 are alternate exterior
angles.
S <3 is congruent to <6
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<2 and <7 are alternate interior
angles.
S <2 is congruent to <7