Geometry Problem 1378: Parallelogram, Diagonal perpendicular to a side,
Distances from a Point to Vertices, Measurement.

Proposition

In the figure below,
ABCD is a parallelogram so that BD is perpendicular to AB. F is any point,
FA = a, FB = b, FC = c, FD = d, and AB = e. Prove that a^{2} + c^{2} = b^{2} + d^{2}
+2(e^{2})