Coplanar Lines in Geometry: Definition & Overview

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  • 0:01 Definition of Coplanar Lines
  • 0:37 Non-Coplanar Lines
  • 0:52 Three-Dimensional Space
  • 2:02 Identifying Coplanar Lines
  • 3:16 Lesson Summary
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Lesson Transcript
Instructor: Yuanxin (Amy) Yang Alcocer

Amy has a master's degree in secondary education and has taught math at a public charter high school.

This lesson will show you how to identify lines that are coplanar in any shape you are given. You will also learn which lines are non-coplanar, and how you can tell the two apart.

Definition of Coplanar Lines

Coplanar lines are lines that lie on the same plane. Picture a giant sheet of paper. Whatever lines are drawn on that sheet of paper will be coplanar because they are lying on the same plane, or the same flat surface. Look at this image.

Rectangular box

Imagine that the blue and white box is solid, and that the dashed green lines are drawn on the front-facing exterior of the box. The two dashed green lines on the one surface of the box above are coplanar because they both lie on the same flat surface.

Non-Coplanar Lines

Lines that do not lie on the same surface or plane are non-coplanar. Look at this image. The red dashed line is non-coplanar with the other two green dashed lines because they lie on different planes, or different surfaces.

Rectangular box with green lines and red lines marked on different sides

3-Dimensional Space

When dealing with coplanar lines, you are working in the 3-dimensional space. The box I've drawn for you is a 3-dimensional shape. A plane is 2-dimensional, so anything that is 2-dimensional in nature will be coplanar because there is only one plane in the 2-dimensional space. Think about that piece of paper. Whatever you draw on it will be 2-dimensional, and everything on it is coplanar because everything is connected by the flat sheet of paper.

When we need to check whether two lines are coplanar, we need to look at the 3-dimensional space; otherwise, there is nothing to check. Only in the 3-dimensional can you have more than one plane. Planes can be parallel to each other or they can intersect each other. Looking at the box again, let's look at where the planes are. Where are the planes in this box?

Each surface of the box is a plane - the diagonals are also. Imagine taking a knife and cutting the box diagonally. The resulting surface is also a plane. If you slice the box in slices like sliced bread, you will also end up with a number of planes or flat surfaces.

Identifying Coplanar Lines

The trick to identifying coplanar lines is if you can take a sheet of paper and make it connect the lines without bending or folding it. For example, look at this diagram. Which lines are coplanar?

Rectangular box with corners labeled

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