The fact that this method works is related to the SSS method of proving triangles congruent.
As you work through the following steps, refer to the figure:
- Draw a working line, l, with a point J on it.
- 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).
- 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.
- Construct a. Arc (D, DF) b. Arc (J, DF)
- Construct a. Arc (E, EF) b. Arc (K, EF) intersecting arc (J, DF) at point L
- Draw segments JL and KL and you’re done.