Problem 539: Right Triangle, Square, Parallel, Perpendicular, Dissection, Area, Pythagoras. Level: High School, SAT Prep, College

The figure shows a right triangle ACB with the square ABDE. AG and DH are parallel to line CBF. Line EHG and DF are parallel to AC. Prove that areas of the square ABDE and the region ACFDHG are equal.