Constructing a triangle with given sidelengths
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In this exercise you are given a point \(P\) on a line, and three line segments (coloured in green). Your task is to construct a point \(Y\) on the line and another point \(Z\) such that the triangle \(\Delta XYZ\) has sidelengths equal to the three green line segments.
The compass tool from the transferring lengths exercise will be very useful.
The diagram contains an example of a point \(P\) on the line and three line segments \(AB\), \(CD\) and \(EF\). The triangle \(\Delta PQR\) has sidelengths \(|PQ| = |AB|\), \(|PR| = |CD|\) and \(|QR| = |EF|\).
Hint. This exercise is explained in Euclid Book I, Proposition 22.
