Basic Constructions

Contributor: Marlene Vogel. Lesson ID: 11283

Are you lost when it comes to using a compass? A geometry compass, that is! They can be used to draw basic math constructions, and even artwork! Ms. Mars shows you step-by-step steps to creative fun!


Congruence, Transformations, Similarity, Plane Geometry (2D)

learning style
Kinesthetic, Visual
personality style
Otter, Beaver
Grade Level
High School (9-12)
Lesson Type
Dig Deeper

Lesson Plan - Get It!

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Compass Artwork

  • Who said math wasn't a creative subject?

Let's disprove that notion.

Download the Compass Artwork document from Downloadable Resources in the right-hand sidebar. By the time you finish this lesson, your creative juices will be flowing!


Take a moment to look at the document.

Don't do anything yet, just look.

  • Does anything come to mind?
  • Do you think this is all strictly technical?

Now, it's time to get started!

Below is a list of vocabulary words that you need to be familiar with for this lesson.

  • Construction is the act of using a compass and straightedge to make a geometric figure.
  • Compass is a geometric tool used to draw circles and arcs.
  • Straightedge is a ruler without markings.
  • Arc is a connected section of a circumference of a circle.

The purpose of this lesson is to continue to add to your geometry vocabulary, help you become familiar with how to use a compass and a straightedge, and teach you how to draw the four basic constructions.

Before you begin drawing any of the constructions, it is important for you to understand the different parts of a compass and how to use it.

geometry compass

Above is a picture of a geometry compass.

Notice that this geometric tool has a point on the end of one leg, a pencil inserted into the other leg, and a knob where the pencil is inserted.

Also, notice that the compass has a black handle sticking out from the top. The two legs of a compass have the ability to spread farther apart or come closer together.

Use your own compass to see how easy it is to make the legs farther apart, then bring them closer together (Note: the point on the one leg can hurt, so avoid touching it.).

When you are getting ready to use your compass to draw a construction, you should go through a couple of steps:

  1. Make sure the pencil has a point on the end so it will make a clean mark.
  2. If your pencil needs to be sharpened, simply turn the knob on the pencil leg and loosen the pencil until it comes out easily. Then, sharpen the pencil, replace it into the holder, and tighten the knob.
  3. Prior to using your compass, make sure the point of your pencil and the point on the other leg are equal.

The following information contains the four basic constructions — and short activities with each — so you can try working with your compass. Before starting the activity, discuss with your teacher the definitions of segment and ray.

Congruent Segments

This basic construction activity will help you learn how to draw two congruent segments:

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Congruent Angles

This basic construction will teach you how to draw two congruent angles:

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Perpendicular Bisector

This basic construction will teach you how to draw a perpendicular bisector for a segment:

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Angle Bisector

This last construction will show you how to draw an angle bisector and split the angle into two congruent angles:

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The following Got It? section offers activities for you to practice your new skills.

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