In square \(ABCD\), \(E\)and \(F\) are the midpoints of \(\overline{BC}\) and \(\overline{CD}\), respectively. Line segments \(\overline{BF}\) and \(\overline{AE}\) intersect at \(G\). Let \(M\) be the midpoint of \(\overline{AB}\), and let \(N\) be the intersection of \(\overline{AE}\) and \(\overline{DM}\).
Here's a picture of the shape (very dark) ------> https://latex.artofproblemsolving.com/5/b/b/5bb0805c0a16bc7d475913c0741cc0aa5509bd6b.png
(a) Show that quadrilaterals \(GFDN\) and \(GBMN\) are trapezoids.
(b) Find the ratios \(BG : MN, FG : MN,\) and \(DN : MN\).
(c) Compute the ratio of the area of the quadrilateral \(GFDN\) to the area of quadrilateral \(GBMN\).
Thank you.
