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ZingPath: Planes

The Definition of a Plane

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The Definition of a Plane

Geometry

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You will get to learn what planes are–and how they relate to lines and points.

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Now You Know

After completing this tutorial, you will be able to complete the following:

  • Know the definition of a plane.
  • Know that three non-collinear points determine a plane.
  • Know that two non-coincident lines determine a plane.
  • Know that a line and point not on the line determine a plane.

Everything You'll Have Covered

What is the definition of a plane? How do we represent and name planes?

~ A plane is a flat object that extends infinitely along its edges, but has no thickness. We typically represent planes with a parallelogram and name them with capital letters.

What are some examples of physical objects that can be modeled by planes? What do we call these objects?

~ Answers may vary. The surface of walls, floors, windows, and tabletops can be thought of as parts of a plane. We call such objects planar figures or planar surfaces.

What are some ways to form a plane?

~ The Animation describes four ways to form a plane:

1.    Any three non-collinear points determine a plane.

2.    A line and a point outside this line determine a plane.

3.    Two parallel lines determine a plane.

4.    Two intersecting lines determine a plane.

Notice that 2-4 are all special examples of 1.

Can you think of an explanation for why a stool or table with three legs will never wobble, while a stool or table with more than three legs might wobble?

~ Answers may vary. The points at the ends of the legs of a three-legged stool or table determine exactly one plane. For this reason, when a three-legged stool or table is placed on a planar surface, such as the floor, it will always sit flat. When a table or stool has more than three legs, the points at the ends of any three of the legs will determine a single plane, but different combinations of legs may determine different planes. When placed on a planar surface, such as the floor, a table or stool with more than three legs will wobble as different combinations of its legs determine different planes.

Tutorial Details

Approximate Time 2 Minutes
Pre-requisite Concepts Students should be able to define a 2-dimensional shape, collinear points, and coincident lines.
Course Geometry
Type of Tutorial Animation
Key Vocabulary 2-dimensional shape, collinear points, coincident lines