How to Copy a Triangle Using a Compass

When you copy a triangle, the idea is to use your compass to “measure” the lengths of the three sides of the given triangle and then make another triangle with sides congruent to the sides of the original triangle.

The fact that this method works is related to the SSS method of proving triangles congruent.

Here is the proof diagram.

As you work through the following steps, refer to the figure:

1. Draw a working line, l, with a point J on it.
2. Put your compass point on point D and open it to the length of DE. The best way to make sure you’ve opened it to just the right amount is to draw a little arc that passes through E. In other words, draw arc (D, DE).
3. Being careful not to change the amount of the compass’s opening from Step 2, put the compass point on point J and construct arc (J, JK) intersecting line l. You have now constructed segment JK on line l that’s congruent to segment DE.
4. Construct a. Arc (D, DF) b. Arc (J, DF)
5. Construct a. Arc (E, EF) b. Arc (K, EF) intersecting arc (J, DF) at point L
6. Draw segments JL and KL and you’re done.