http://www.ck12.org Chapter 3. Parallel and Perpendicular Lines
Skew linesare 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.
Atransversalis a line that intersects two distinct lines. These two lines may or may not be parallel. The area
between landmis the called theinterior. The areaoutside landmis called theexterior.
TheParallel Lines Propertyis a transitive property that can be applied to parallel lines. It states that if linesl||m
andm||n, thenl||n.
Example A
Are linesqandrparallel?
First find ifp||q, followed byp||r. If so, thenq||r.
p||qby the Converse of the Corresponding Angles Postulate, the corresponding angles are 65◦. p||rby the
Converse of the Alternate Exterior Angles Theorem, the alternate exterior angles are 115◦. Therefore, by the Parallel
Lines Property,q||r.
Example B
In the cube below, list 3 pairs of parallel planes.
PlanesABCandEF G, PlanesAEGandF BH, PlanesAEBandCDH
Example C
In the cube below, list 3 pairs of skew line segments.
BDandCG,BFandEG,GHandAE(there are others, too)
Watch this video for help with the Examples above.
MEDIA
Click image to the left for more content.CK-12 Foundation: Chapter3ParallelandSkewLinesB
Vocabulary
Two or more lines areparallelwhen they lie in the same plane and never intersect.Skew linesare lines that are in
different planes and never intersect. Atransversalis a line that intersects two distinct lines.
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.
- Find two pairs of skew lines.
- List a pair of parallel lines.