Points, Lines, and Planes

Contributor: Marlene Vogel. Lesson ID: 10906

Points, lines, and planes are the "stars" of geometry, and they are all around us! Learn important vocabulary words and simple concepts, then create your own artwork to display what you've learned!


High School

learning style
personality style
Beaver, Golden Retriever
Grade Level
High School (9-12)
Lesson Type
Dig Deeper

Lesson Plan - Get It!


Constellations are a great way to learn about points, lines, and planes!

Below is a photo of the night sky as we see it and then one with the constellation lines added.

  • Do you think you could draw the lines to make the correct picture of a constellation?

Try it out with the Constellations document found under Downloadable Resources in the right-hand sidebar!

Vocabulary Look up these definitions at Mathwords.com, and be sure to write them down and even memorize them!

  • collinear
  • coplanar
  • line
  • plane
  • point
  • postulate

Although you now have the definitions of the vocabulary words listed above, sometimes math terms are easier to understand when put into an explanation. The following is a discussion concerning how the vocabulary words above relate to each other and geometry:

A point can be thought of as a location. Consider your computer screen. If you place your finger on it, you have just identified a point. If you move your finger to another place on your computer screen, then you have located another point. You use a capital letter whenever labeling a point in geometry. Points are located everywhere!

A series of points is a line. A line extends in both directions indefinitely. You label a line by listing two of the points found on it. All points located on the same line are referred to as being collinear.

A plane is flat surface that extends in all directions. It is very important to note that a plane does not have any thickness. You label a plane simply with one capital letter, or by naming 3 non-collinear points on the plane.

Finally, all lines and points located on the same plane are referred to as coplanar.

A postulate is a statement in math that is accepted as true. It does not need to be proven. Below are 4 postulates and an example of each. You may recognize them from your algebra lessons.

  • Postulate 1-1: Through any two points there is exactly one line.
  • Postulate 1-2: If two lines intersect, then they intersect in exactly one point.
  • Postulate 1-3: If two planes intersect, then they intersect in a line.
  • Postulate 1-4: Through any three non-collinear points there is exactly one plane.

The next two sections of the lesson offer opportunities for you to expand your knowledge of the above geometric terms and postulates.

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