Online Math: Geometry Problem 1185:
Similar Rectangles, Four Quadrilaterals, Sum of Areas, Metric Relations. Level: School, College. Tiled
background image: Nazca Lines: El Condor.

The figure shows the similar
rectangles ABCD
and EFGH (angle ACB = angle EGF). S_{1}, S_{2}, S_{3}, and S_{4}, are the
areas of the shaded quadrilaterals. Prove that:
(1) AE^{2} + CG^{2} = BF^{2} + DH^{2}; (2) S_{1} + S_{3} = S_{2} + S_{4}.