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 a² + c² = b² + d² +2(e²) 

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