Equal alternate angles are used to construct which of the following?

From the figure, we can see that a line P passes through two lines L and M, making angles x, y, g, and h.

Only two parallel lines with a transversal passing through, give the concept of alternate angles and corresponding angles. 

So, from the concept of transversal, 
$\begin{array}{c}\angle \mathrm{x} = \angle \mathrm{y} ....(\mathrm{alternate} \mathrm{angles})\\ \angle \mathrm{g} = \angle \mathrm{h} ....(\mathrm{corresponding} \mathrm{angles})\end{array}$

Which signifies that line L is parallel to line M.

Thus, Equal alternate angles are used to construct a line parallel to a given line.