Parallel and Skew Lines
Bill Zahner
Lori Jordan
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Printed: May 4, 2016
AUTHORS
Bill Zahner
Lori Jordan
www.ck12.org
C HAPTER
Chapter 1. Parallel and Skew Lines
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Parallel and Skew Lines
Here you’ll learn about parallel and skew lines.
What if you were given a pair of lines that never intersect and were asked to describe them? What terminology
would you use? After completing this Concept, you will be able to define the terms parallel line, skew line, and
transversal. You’ll also be able to apply the properties associated with parallel lines.
Watch This
MEDIA
Click image to the left or use the URL below.
URL: https://www.ck12.org/flx/render/embeddedobject/136881
CK-12 Foundation: Chapter3ParallelandSkewLinesA
Watch the portions of this video dealing with parallel lines.
MEDIA
Click image to the left or use the URL below.
URL: https://www.ck12.org/flx/render/embeddedobject/1341
James Sousa: Parallel Lines
MEDIA
Click image to the left or use the URL below.
URL: https://www.ck12.org/flx/render/embeddedobject/1342
James Sousa: Parallel Line Postulate
Guidance
Two or more lines are parallel when they lie in the same plane and never intersect. The symbol for parallel is ||. To
mark lines parallel, draw arrows (>) on each parallel line. If there are more than one pair of parallel lines, use two
←
→ ←→
arrows (>>) for the second pair. The two lines below would be labeled AB || MN or l || m.
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For a line and a point not on the line, there is exactly one line parallel to this line through the point. There are
infinitely many lines that pass through A, but only one is parallel to l.
Skew lines are lines that are in different planes and never intersect. The difference between parallel lines and skew
lines is parallel lines lie in the same plane while skew lines lie in different planes.
A transversal is a line that intersects two distinct lines. These two lines may or may not be parallel. The area
between l and m is the called the interior. The area outside l and m is called the exterior.
The Parallel Lines Property is a transitive property that can be applied to parallel lines. It states that if lines l || m
and m || n, then l || n.
Example A
Are lines q and r parallel?
Notice that the arrow markings indicate that p || q. Similarly, arrow markings indicate that p || r. This means that
q || r by the Parallel Lines Property.
Example B
In the cube below, list 3 pairs of parallel planes.
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Chapter 1. Parallel and Skew Lines
Planes ABC and EFG, Planes AEG and FBH, Planes AEB and CDH
Example C
In the cube below, list 3 pairs of skew line segments.
BD and CG, BF and EG, GH and AE (there are others, too)
Watch this video for help with the Examples above.
MEDIA
Click image to the left or use the URL below.
URL: https://www.ck12.org/flx/render/embeddedobject/136882
CK-12 Foundation: Chapter3ParallelandSkewLinesB
Guided Practice
Use the figure below to answer the questions. The two pentagons are parallel and all of the rectangular sides are
perpendicular to both of them.
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1. Find two pairs of skew lines.
2. List a pair of parallel lines.
3. For XY , how many parallel lines would pass through point D? Name this/these line(s).
Answers:
1. ZV and W B. Y D and VW
2. ZV and EA.
3. One line, CD
Interactive Practice
MEDIA
Click image to the left or use the URL below.
URL: https://www.ck12.org/flx/render/embeddedobject/113005
Explore More
1. Which of the following is the best example of parallel lines?
a.
b.
c.
d.
Railroad Tracks
Lamp Post and a Sidewalk
Longitude on a Globe
Stonehenge (the stone structure in Scotland)
2. Which of the following is the best example of skew lines?
a.
b.
c.
d.
Roof of a Home
Northbound Freeway and an Eastbound Overpass
Longitude on a Globe
The Golden Gate Bridge
For 3-10, determine whether the statement is true or false.
3. If p||q and q||r, then p||r.
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4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
Chapter 1. Parallel and Skew Lines
Skew lines are never in the same plane.
Skew lines can be perpendicular.
Planes can be parallel.
Parallel lines are never in the same plane.
Skew lines never intersect.
Skew lines can be in the same plane.
Parallel lines can intersect.
Come up with your own example of parallel lines in the real world.
Come up with your own example of skew lines in the real world.
What type of shapes do you know that have parallel line segments in them?
What type of objects do you know that have skew line segments in them?
If two lines segments are not in the same plane, are they skew?
Answers for Explore More Problems
To view the Explore More answers, open this PDF file and look for section 3.1.
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