3-1 Parallel Lines and Transversals
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Transcript of 3-1 Parallel Lines and Transversals
3-1 Parallel Lines and Transversals3-1 Parallel Lines and Transversals3-1 Parallel Lines and Transversals3-1 Parallel Lines and Transversals
Page 173Page 173
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 LinesParallel lines are lines in the same plane that never intersect.
-8 -6 -4 -2
2
42 6 8
4
6
-4
-6
-8
-2
8
Parallel lines have the same slope.
Example 1Determine whether these lines are parallel.y = 4x -6
and y = 4x + 2
The slope of both lines is 4.
So, the lines are parallel.
Skew Lines
Skew lines are lines that do not intersect and are not coplanar.
A
B
m
n
B. Name a segment skew to EH.
Answer: AB, CD, BG, or CF
Parallel Planes
Parallel planes are planes that do not intersect.
A
B
C. Name a plane parallel to plane ABG.
Answer: plane CDE
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Transversal DefinitionA transversal is a line that
intersects two coplanar lines at two different points.
Exterior
Exterior
Interior
1 234
5 6
78
r
s
Transversal t
Angles formed by Transversals
Consecutive interior angles
5&4
1 2
34
5 6
78
6&3
interior
Angles formed by Transversals
Alternate interior angles
6&4 5&3
1 2
34
5 6
78
interior
Angles formed by Transversals
Alternate exterior angles
7&1
1 2
34
5 6
78
8&2
exterior
exterior
Angles formed by Transversals
Corresponding angles
5&1
1 2
34
5 6
78
6&2 7&3 8&4
Classify Angle Pair Relationships
A. Classify the relationship between 2 and 6 as alternate interior, alternate exterior, corresponding, or consecutive interior angles.
Answer: corresponding
B. Classify the relationship between 1 and 7 as alternate interior, alternate exterior, corresponding, or consecutive interior angles.
Answer: alternate exterior
C. Classify the relationship between 3 and 8 as alternate interior, alternate exterior, corresponding, or consecutive interior angles.
Answer: consecutive interior
D. Classify the relationship between 3 and 5 as alternate interior, alternate exterior, corresponding, or consecutive interior angles.
Answer: alternate interior
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.
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.