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General Studies Math: Help & Review8 chapters | 85 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.

This lesson will help you understand the geometry concept of a plane. We will discuss how to name planes and look at some example problems. Then, you can check your understanding with a quiz.

In geometry, a **plane** is a flat surface that extends forever in two dimensions, but has no thickness. It's a bit difficult to visualize a plane because in real life, there is nothing that we can use as a true example of a geometric plane. However, we can use the surface of a wall, the floor, or even a piece of paper to represent a part of a geometric plane. You just have to remember that unlike the real-world parts of planes, geometric planes have no edge to them.

In algebra, we graph points in the **coordinate plane**, which is an example of a geometric plane. The coordinate plane has a number line that extends left to right indefinitely and another one that extends up and down indefinitely. You can never see the entire coordinate plane. The fact that it extends forever along the *x*- and *y*-axis is just indicated by arrows on the ends of the number lines. Those are the two dimensions over which a plane extends forever. When you graph points, you never graph one point deeper into the paper than another point. That shows that the coordinate plane does not have thickness to it.

In order for us to discuss planes, we need to be able to see them and label them. Therefore, even though geometric planes do not have to edges to them, when they are drawn, they have an outline. Usually, they are represented by a parallelogram that is shaded in, like this:

If we want to talk about two or more different planes, then we need to be able to name each plane. There are two ways to label planes. Most frequently, you use three or four of the points that are in the plane as the name. Remember that points are indicated with a dot and are labeled with a capital letter. The second way to name a plane is with just one capital letter that is written in the corner of the image of the plane. This letter does not have a dot next to it and is sometimes written in a script font that is different from the font used for points.

Now let's go through some example questions to help you understand which points are in a plane and how to use them to name the plane.

Look at this image:

Now think about the answers to these three questions, and I'll explain the answers shortly.

- What points are in the plane?
- What point is not in the plane?
- What are three different names for the plane?

Now, let's talk about the answers.

- What points are in the plane?

The points in the plane are indicated by a dot and a capital letter and are within the outline of the parallelogram. So, points*E*,*L*,*A*, and*N*are all in the plane. Remember that the edge and the corners of the parallelogram are only there to help visualize the plane. So, points*E*and*N*are completely in the plane because the outline is not really the edge of the plane. A geometric plane does not have edges or corners since it extends forever. - What point is not on the plane?

Point*S*is not in the plane. Since it is not contained within the outline of the plane, you can imagine that it is floating above the plane. You can picture it as if the blue plane is the floor of a room and point*S*is a soap bubble floating through the room, therefore*S*does not touch the plane. Points*E*,*L*,*A*, and*N*would all be bubbles that have landed on the floor. - What are the different names for the plane?

The easiest name for the plane would be*P*. We know that*P*is not a point because it does not have a dot next to it and because the font is a little different from the font used for the points. To give the plane other names, you can use any 3 or 4 points in the plane. So,*ELAN*would be another name, no matter in which order you list those letters. Another name could be*NAL*or*LEA*.

A **plane** is a flat surface that extends forever in two dimensions, but has no thickness. Planes have no edges to them. However, in diagrams, a plane will be shown as an outline of a parallelogram. Planes can be named with a single capital letter or with 3 or 4 points that are contained in the plane. Points that are not contained within the outline of the plane are assumed not to be in the plane.

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General Studies Math: Help & Review8 chapters | 85 lessons

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