Triangles from folding

Using a square piece of paper, label each side 1 unit long. Find the midpoint of the top side by folding in half. Take the bottom right corner and fold it up to touch the midpoint of the top side. This creates three triangles. ABC, CDE, EFG. Determine the side lengths of all three triangles.

This was a nifty little problem given by Harold Jacobs at Asilomar 2007.