Cutting off a length equal to a shorter line segment

Now that you have done the Transferring a length from one point to another construction, you can use the compass tool in the applet below.

In this exercise you are given two line segments \(WX\) and \(YZ\) with \(WX\) longer than \(YZ\). Your task is to construct a point \(V\) on \(WX\) such that \(|WV| = |YZ|\). The diagram contains an example of two line segments \(AB\) and \(CD\) with \(|AB| > |CD|\) and a point \(E\) on \(AB\) such that \(|AE| = |CD|\).

This exercise is made significantly easier now that you can use the compass tool from the previous exercise.

Hint. This exercise is explained in Euclid Book I, Proposition 3.