Problem #PRU-53749

Problem

In the trapezium \(ABCD\) the point \(E\) is the point of intersection of the sides \(AB\) and \(CD\), the point \(G\) is the point of intersection of diagonals, the points \(F,H\) are the midpoints of the sides \(BC\) and \(AD\) respectively.

Prove that the points \(E,F,G,H\) lie on one line.