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Midpoint of square's diagonal - proof

Hi All,

I am not able to solve this geometry problem correctly. Visually it looks plausible but how do you go about proving it.

Attachment 21159

In the diagram, ABCD is a square, EFG is an isosceles triangle, Angle EFG = 90, and M is midpoint of EG.

(a) Show that Angle EFA = Angle FGB.

(b) Explain why Triangle AFE, and BGF are congruent.

(c) If AC is drawn, explain why M is the midpoint of AC.

Also one more question! Is there a way to describe such geometry problems in latex? I did the the attachment in mspaint, was wondering if there is a better way? Thanks for your help!