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.
- Using your straightedge, draw a working line, l, with a point P anywhere on it.
- 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).
- 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.