We’re working on geometric constructions in 6th and 7th grade this month, so I’m going to share with you some basic constructions, as well as related activities and example projects from my students.

To begin with, we’ll simply draw a line segment and use our compass to construct a congruent, or matching, segment.  This technique can be used to copy any segment (or any side of a polygon) without measuring its length.

1. Begin with a line segment you wish to copy.  Make a point to use as the first endpoint of your new segment.
2. Set the length of the compass so that one side is on each endpoint of your original segment.
3. Keep the compass set to that length, transfer it to the endpoint of your new segment.
4. Draw an arc using that point as its center.
5. Use a straight edge to connect your endpoint to anywhere on the arc.
6. Congratulations!  You now have two congruent segments!

This very simple construction illustrates an important geometric concept: the definition of a circle.  A circle is a set of points such that all are equidistant from a center point.  The length to which we have set our compass is the radius of our circle, so if we connect its center to any point on the circle, we will have another segment of the same length, i.e. a congruent segment.