# Monge's Theorem

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8. Describe how you might explain the straight-edge and compass construction of the tangent to the circle to your high school students. Write a one to two page description of such a lesson. Make a web page for this lesson and include some sketchpad pictures as illustrations for a lesson.

Explanation of construction:

Using a compass and straight edge, we will be constructing a tangent to a circle. As the construction steps are given, they will be illustrating on the board (or on a projected computer screen, if you have the resources).

To start your construction, make two vertices, A and B, somewhere near the center of your paper. Construct a circle using point A as center so that point B lies outside the circle. Name the circle c1. Draw a line segment with end points A and B.

Now, find the midpoint of segment AB. (Ask for a volunteer to demonstrate this, as it should be previously learned information. If there are no volunteers, demonstrate it yourself.) Please watch me demonstrate this before you do it. Set your compass point on A and draw an arc through the B. Using the same radius on your compass, perform the same construction using B as the arc center. Make sure that the two arcs cross. Mark the intersections of the arcs as vertices C and D. Go ahead and try this.

Draw a segment using C and D as endpoints. Mark the point where AB and CD cross as E. Using E as the center. Make a arc of radius AE that crosses c1 twice. Mark the intersections of the arc with c1 as F and G. Draw a line through F and B and another through G and B. Label these lines as t1 and t2, your tangent lines to c1. Your construction is now complete!

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There is also a lesson with illustrations for you to view.

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