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!

categories

High School

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

Lesson Plan - Get It!

Audio:

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!

compass art

Take a moment to look at the document.

Don't do anything yet, just look.

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

Share your thoughts with your parent or teacher.

Now, it's time to get started!

Below is a list of vocabulary words that you need to be familiar with for this lesson. You can find their definitions at Mathwords.com. Write them down and even memorize them!

  • construction
  • compass
  • straightedge
  • arc

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, 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.

  1. Congruent Segments This basic construction activity will help you learn how to draw two congruent segments.
    1. Use your straightedge to draw a 2-inch line segment. Label the points A and B.
    2. Below your line segment, draw a ray. Make the ray longer than the line segment. Label the point on the ray C.
    3. Take your compass and put the pointed end on point A of your line segment. Open your compass until the point of the pencil is on point B of your line segment. You have now found the measurement of your line segment with your compass.
    4. Grab your compass by the top handle and lift it off your line segment. You want to grab it by the top handle so that you do not move either of the legs and mess up your measurement.
    5. Place the pointed end of the compass on point C of your ray. When you do that, your pencil point will also land on a part of the ray. Be very careful not to move the legs.
    6. Use one hand to hold the pointed end of the compass on point C and the other hand to grab the top handle. Using the top handle, move the pencil so you draw an arc across your ray (See below):
    7. Take your pencil and make a dot on ray C. You have made ray C congruent with line segment AB!
  2. Congruent Angles This basic construction will teach you how to draw two congruent angles.
    1. Draw an angle using two rays that share the same endpoint A. Use your straightedge and pencil.
    2. Use your straight edge and pencil to draw ray S below angle A.
    3. Place the point of your compass on point A of your angle and open your compass wide enough that, when you put the pencil part of your compass on the paper, it is still touching one of the rays that makes up angle A. Draw an arc that crosses both of the rays that make up angle A.
    4. Put your compass down and pick up your pencil. Draw a point (dot) at each place where the arc intersects the angle. Label each point B and C.
    5. Again, put your compass point on point A of your angle and put the pencil point on point C. Grab your compass from the top handle and move it to ray S.
    6. Put the compass point on point S of your ray. Hold the point with one hand and grab the top handle of the compass with the other hand. Draw an arc that intersects ray S; however, make the arc large enough so that when you go to turn ray S into an angle, the arc will cross another ray.
    7. Use your pencil to make a point (dot) where the arc intersects ray S. Label that point R.
    8. Use your compass to get the measurement between points B and C on angle A. Put the point of the compass on point B. Open the compass and put the pencil point on point C.
    9. Grab the compass at the top handle and lift it off angle A.
    10. Put the point of the compass on point R of ray S. Use one hand to hold the point in place and the other hand to draw an arc across the first arc drawn on ray S (See below.).
    11. Use your straightedge to draw a ray that begins at point S and goes through where the two arcs intersect. Draw a point (dot) where the line goes through the two intersecting arcs and label it T.
    12. You have now drawn an angle that is congruent to angle A!
  3. Perpendicular Bisector This basic construction will teach you how to draw a perpendicular bisector for a segment.
    1. Use your pencil and straightedge and draw a line segment. Label the endpoints A and B.
    2. Get your compass and put the point of the compass on point A. Open your compass so the pencil lands on line segment AB, a little past the halfway mark. Draw an arc that intersects segment AB. Make sure you use one hand to hold the point of the compass on point A and another hand to move the pencil part of the compass to make the arc.
    3. Be careful not to change the legs on the compass. Grab your compass from the top handle and lift it off of line segment AB. Turn your compass around and put the point of the compass on point B of line segment AB, use one hand to hold it in place, and use your other hand to draw another arc that intersects line segment AB. When you are finished, you will notice that the second arc also intersects the first arc at the top and the bottom.
    4. Use your straightedge and pencil and draw a perpendicular line through the two places where the arcs intersect each other.
    5. You have successfully drawn a perpendicular bisector!
  4. Angle Bisector This last construction will show you how to draw an angle bisector and split the angle into two congruent angles.
    1. Use your straightedge and pencil and draw an angle with a shared endpoint C.
    2. Take your compass, put the point end on point C of your angle, open the legs, and draw an arc that intersects both rays of the angle.
    3. Use your pencil and draw a point (dot) at each place where the arc intersects the angle. Label the points D and E.
    4. Put the point of your compass on point D and open your compass wide enough that you can draw an arc inside, but not intersecting, the rays of the angle. Carefully lift your compass by the handle so you keep it open to the same measurement, put the point of the compass on point E, and draw an arc inside, but not intersecting, the rays of the angle. When you have completed this step, your two arcs should resemble an "x."
    5. Use your straightedge to draw a ray that begins at point C and goes through where the two arcs intersect.
    6. Congratulations! You have just bisected an angle! Now you can use this skill in the future to help you in activities such as measurements of angles.

The following Got It? section offers activities for you to use to practice your new skills. You can choose to complete one or all of the activities.

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