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1.10 How to Use a Compass

 

Blueprint icon  Blueprints for this Lesson:
 
  • Use a compass and a straight edge to measure distances.

Foundational icon Foundational Knowledge:

Draw the following items using a pencil and a straight edge.  The size of these figures doesn’t matter, just the features of the item and the labeling.  When you are finished, check your drawings to see if they are correct.

  1. Opposite rays Ray P R and Ray P Q
  2. Line M N with a midpoint O.
  3. Angle X W Y

check your answersClick here to check your answers.

Framework for Understanding:

Architects use construction tools in their design work. They need more than a ruler and graph paper; they use tools like a compass and a protractor to help them construct angles and measure them. In architecture, blueprints can be created prior to the actual construction.  These may be drawn by hand using specialized tools or with a computer program.  At construction sites, the builders may need to create a quick sketch.  They may not have the tools of precision available, so a quick drawing can be used.  Drawings are typically created using only a straightedge and pencil. As a Geometry student, it is very important that you learn to use these same tools. In this lesson we are going to introduce the compass and learn how to work with it.

Throughout this course, you will be asked to use your compass and a straightedge to create various geometric constructions. Later, you will also learn to use a software construction tool to do what our handheld compasses do. This is one of the most exciting parts of any geometry course, so let's get started.

 

CompassIf you have never practiced using a compass, spend some time drawing circles of various radii. If the beginnings and ends of the circles connect exactly, you've got it. If they are not connecting smoothly, here are some pointers to help you properly use your compass. 


  • Be sure the pencil tip is sharp and lines up with the metal tip when the compass is closed completely.
  • If the arms of the compass are easily moved in and out and cannot be tightened, get a new compass.
  • It is easier for the metal tip to "grip" the paper if there are several sheets of paper underneath the top sheet. Try putting a notebook underneath the paper.
  • When drawing, keep most of the pressure on the metal tip and allow the pencil tip to glide around smoothly.
  • Hold the compass at the top, not around its arms.

Using a Compass

We will use a compass to do more than make pretty circles.  Try this construction with your own compass.

Construct a Segment Congruent to a Given Segment

Directions: 

  1. Use your straightedge to draw a segment AB.  Label the endpoints of the segment.  (This will be the segment that you will copy).
    line segment A B
  2. Draw a ray with endpoint X.  Make sure it is longer than line segment A B.
    ray with endpoint X
  3. Open your compass to the length of line segment A B.  (You will place the tip of your compass on point A and the pencil on point B.)
  4. With the same compass setting, put the compass point on point X.  Draw an arc that intersects the ray. 
    ray X Y with endpoint at Xcompass
  5. Label the point of intersection Y. You have just constructed a congruent segment!
    ray X Y with endpoint at Xcompass

Justification:  Since you used AB for the opening of your compass, the transferred length onto the ray makes line segment A B is congruent to line segment X Y.

Construct a Segment Bisector 

Directions:

  1. Use your straightedge to draw segment AB.  Label the endpoints of the segment.
    segment A B
  2. Place your compass point on A and stretch the compass MORE THAN half way to point B.
  3. With this length, swing a large arc that will go BOTH above and below Segment A B . Without changing the opening on the compass, place the compass point on B and swing the arc again. The two arcs you have drawn should intersect.
    Two arcs intersect above and below section A B
  4. With your straightedge, connect the two points of intersection.
    Two arcs intersect above and below section A B, and one line connects the two points of the intersection.
  5. This vertical line bisects Segment A B. Label the point where the new line and Segment A B cross as M.
    Two arcs intersect above and below section A B, and the line that connects the two points of the intersection intersect with section A B. The point of the intersection is the bisecting point M

Segment AB has now been bisected and AM = MB. (It could also be said that they are congruent.)

Important iconNOTE: If you do not wish to make a "large" arc in step 3, you may simply place one small arc above Segment A B and one small arc below Segment A B.

Since the intersection of the two arcs are equidistant from A and B, the line that contains the intersection points of the arcs will go directly through the midpoint of the segment.

Construct the perpendicular to a given line through a point on the line

Directions:

  1. Use your straightedge to draw a line, x. Place point P on the line.
    line x that contains point P
  2. Put the compass point on point P. Draw arcs intersecting x in two points. Label the two points A and B.
    line x that contains points A, P and B compass
  3. Open the compass a little wider than the setting you used to create points A and B. With the compass tip on A, draw an arc above point P.
    line x that contains points A, P and B. An arc is drawn above line x exactly in line with P compass
  4. Without changing the opening of your compass, place the compass point on B. Draw an arc that intersects the arc from step 3. Label the point of intersection C.
    line x that contains points A, P and B. Two arcs intersect above line x exactly in line with Pcompass
  5. Draw line C P. This is your perpendicular line.
    line x that contains points A, P and B. Two arcs intersect above line x exactly in line with P. A vertical line is drawn from C to P.

Justification: You constructed points A and B, so that P is equidistant from A and B. Then you constructed point C, so that C is equidistant from A and B. Thus line C P is the perpendicular bisector of line segment A B, and line C P is perpendicular to x at P.

Congratulations, you did it! You know how to use a compass. Now, it is time to move on to some practice.