How to Copy a Line Segment Using a Compass

The key to copying a given line segment is to open your compass to the length of the segment; then, using that amount of opening, you can mark off another segment of the same length.

Here's the proof diagram.

This figure shows the solution; refer to it as you work through the following steps.

1. Using your straightedge, draw a working line, l, with a point P anywhere on it.
2. Put your compass point on point M and open it to the length of line MN. The best way to make sure you've opened it to just the right amount is to draw a little arc that passes through N. In other words, draw arc (M, MN).
3. Being careful not to change the amount of the compass's opening from Step 2, put the compass point on point P and construct arc (P, MN) intersecting line l.

You call this point of intersection point Q, and you're done.