In parallelogram \(EFGH\), let \(M\) be the midpoint of side \(\overline{EF}\) and let \(N \) be the midpoint of side \(\overline{EH}\). Line segments \(\overline{FH}\) and \(\overline{GM}\) intersect at \(P \), and line segments \(\overline{FH}\) and \(\overline{GN}\) intersect at \(Q\). Find \(\frac{PQ}{FH}\).
