How to tell if lines are parallel, perpendicular, or neither?

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It’s time for a little geometry refresher with this quick lesson about parallel and perpendicular lines. These terms come in handy not just in math class but throughout life. Here’s how to tell the difference between them.

Parallel lines

If two lines are parallel to each other, then they have the same slope. This does not refer to their length (one line may be longer than the other), but instead the angle of the lines. Parallel lines never intersect or touch. Some people remember this by the double Ls in the word parallel. The two Ls are parallel to each other.

In gymnastics, the athletes sometimes perform on the parallel bars. If you watch them, you will notice that the two bars are different heights but they have the same gradient so they are parallel.

Perpendicular lines

By contrast, perpendicular lines intersect and form a 90-degree angle. The most basic example would be a graph that shows an X-axis and a Y-axis. The two axis lines meet at the zero value point, creating a 90-degree, or right, angle.

You can see another example of perpendicular lines in the flag of Greece. In the top left-hand corner there are two intersecting white lines. The part where they meet creates a right angle, making them perpendicular to each other.

Lines that are neither parallel nor perpendicular

Two lines may intersect or touch but they do not create a 90-degree angle. In this case, they’re not perpendicular but they’re not parallel either so they’re neither. Furthermore, two lines might be the same length but they don’t share the same slope so they can’t be parallel. Since they don’t intersect, they can’t be perpendicular either.

Now that you know or remember the difference, you’ll start seeing parallel and perpendicular lines everywhere throughout your day!

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