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). S1, S2, S3, and S4, are the
areas of the shaded quadrilaterals. Prove that:
(1) AE2 + CG2 = BF2 + DH2; (2) S1 + S3 = S2 + S4.