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Skew Lines in Geometry: Definition & Examples

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  • 0:00 What Are Skew Lines?
  • 0:30 Examples
  • 3:00 Lesson Summary
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Lesson Transcript
Instructor: Miriam Snare

Miriam has taught middle- and high-school math for over 10 years and has a master's degree in Curriculum and Instruction.

In this lesson, learn the definition of skew lines. You will also learn tips for differentiating skew lines from parallel lines, as well as look at some examples.

What are Skew Lines?

Skew lines are lines that are in different planes, are not parallel, and do not intersect. Parallel lines, as you will recall, are lines that are in the same plane and do not intersect. Also, remember that in mathematics, lines extend forever in both directions.

Since skew lines have to be in different planes, we need to think in 3-D to visualize them. However, it is often difficult to illustrate three-dimensional concepts on paper or a computer screen. Let's look at a few examples to help you see how skew lines appear in diagrams.

Examples

Imagine you are standing in a small room, like a closet. It is so small that you can touch two walls by stretching out your arms. The walls are our planes in this example. You have a marker in each hand. On the wall on your left, you draw a horizontal line. If you draw another horizontal line on the wall to your right, the two lines will be parallel. If you draw any non-horizontal line on your right, then the left and right lines will be skew lines. The following is an illustration of this scenario of skew lines.

Skew lines on the side of a cube

Let's think about a larger example. Imagine you are standing in the middle of a ballroom. The slats of the wooden floor form lines stretching out in front of you and behind you. Overhead is a banner that stretches diagonally from corner to corner across the ceiling, as shown in the illustration on screen. How can you tell if the line of the floor slats and the bottom edge of the banner form skew lines?

Ballroom with banner

A quick way to check if lines are parallel or skew is to imagine you could pull a window shade attached to one line over to the other line. If the window shade has to twist to line up with the second line, then the lines are skew. If the shade stays flat, then it is a plane containing the parallel lines.

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