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High School Geometry: Help and Review13 chapters | 162 lessons

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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.

**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.

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.

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?

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.

Let's try out that idea in our ballroom example. Pretend you could pull that banner down to the floor. That line on the bottom edge would now intersect the line on the floor, unless you twist the banner. Therefore, in the diagram while the banner is at the ceiling, the two lines are skew.

Let's look at one more example that is more abstract than the previous ones. The following is a diagram of a cube labeled with a point at each corner. We draw a line through points *F* and *E*. What are the edges of the cube that are on lines skew to line *FE*?

Any edges that *intersect* the line *FE* cannot be skew. Therefore, *ED*, *EH*, *FG*, and *FA* are *not skew*. Any edges that are *parallel* to line *FE* cannot be skew. Therefore, we can eliminate *DG*, *BC*, and *AH*. That leaves us with the lines *DC*, *BG*, *HC*, and *AB*, each of which is skew to line *FE*.

**Skew lines**are not in the same plane, do not intersect, and are not parallel.**Parallel lines**are in the same plane and do not intersect.- Skew lines can only appear in 3-D diagrams, so try to imagine the diagram in a room instead of on a flat surface.
- Try imagining pulling a window shade from one line to the other. If you have to twist the shade to line it up, then the lines are skew.
- If you can imagine a flat surface stretching between two lines, then they are parallel.

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High School Geometry: Help and Review13 chapters | 162 lessons

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