3-1 Parallel Lines and Transversals

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3-1 Parallel Lines and Transversals
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You used angle and line segment relationships to
prove theorems.

• Identify relationships between two lines or two
  planes.

• Name angle pairs formed by parallel lines and
  transversals.

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Parallel Lines
Parallel lines are lines in the same plane that
never intersect.
Parallel lines have the same slope.
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Example 1
Determine whether these lines are parallel.
y 4x 2
y 4x -6
and
The slope of both lines is 4.
So, the lines are parallel.
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Skew Lines
n
A
m
B

• Skew lines are lines that do not intersect and
  are not coplanar.

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(No Transcript)
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Parallel Planes
A
B

• Parallel planes are planes that do not intersect.

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C. Name a plane parallel to plane ABG.
Answer plane CDE
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Transversal Definition

• A transversal is a line that intersects two
  coplanar lines at two different points.

Transversal t
Exterior
1
2
4
3
r
Interior
5
6
s
8
7
Exterior
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Angles formed by Transversals
1
2
4
3
interior
5
6
7
8
Consecutive interior angles
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Angles formed by Transversals
1
2
4
3
interior
5
6
7
8
Alternate interior angles
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Angles formed by Transversals
1
2
7
8
Alternate exterior angles
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Angles formed by Transversals
1
2
4
3
5
6
7
8
Corresponding angles
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Classify Angle Pair Relationships
A. Classify the relationship between ?2 and ?6 as
alternate interior, alternate exterior,
corresponding, or consecutive interior angles.
Answer corresponding
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B. Classify the relationship between ?1 and ?7 as
alternate interior, alternate exterior,
corresponding, or consecutive interior angles.
Answer alternate exterior
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C. Classify the relationship between ?3 and ?8 as
alternate interior, alternate exterior,
corresponding, or consecutive interior angles.
Answer consecutive interior
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D. Classify the relationship between ?3 and ?5 as
alternate interior, alternate exterior,
corresponding, or consecutive interior angles.
Answer alternate interior
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A. BUS STATION The driveways at a bus station are
shown. Identify the transversal connecting ?1 and
?2. Then classify the relationship between the
pair of angles.
Answer The transversal connecting ?1 and ?2 is
line v. These are corresponding angles.
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B. BUS STATION The driveways at a bus station are
shown. Identify the transversal connecting ?2 and
?3. Then classify the relationship between the
pair of angles.
Answer The transversal connecting ?2 and ?3 is
line v. These are alternate interior angles.