Constructing a parallelogram with area equal to a given triangle and angle equal to a given angle

In this exercise you are given a triangle \(\Delta PQR\) and an angle \(\angle XYZ\). Your task is to construct a parallelogram with area equal to the area of \(\Delta PQR\) and one pair of opposite angles equal to \(\angle XYZ\).

Once you are done you can use the polygon tool to highlight the parallelogram and then use the area tool to check that the area is equal to that of the triangle \(\Delta PQR\). You have a new parallel line tool from the previous construction that will be useful.

The diagram contains an example of a triangle \(\Delta ABC\) and an angle \(\angle DEF\) such that the orange parallelogram \(AGHI\) has area equal to that of \(\Delta ABC\) and \(\angle GAH = \angle DEF\).

Hint. This exercise is explained in Euclid Book I, Proposition 42.