3-1 parallel lines and transversals
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3-1 Parallel Lines and Transversals. Page 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. Page 173. 8. 6. 4. 2. 6. 8. -2. -8. -6. -4. 2. 4. -2. - PowerPoint PPT PresentationTRANSCRIPT
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.
Page 173
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
Page 174
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.