Rectangular Pyramids

Stage: 4 and 5 Challenge Level: Challenge Level:1
Is it true that p 2 + q 2 = s 2 + r 2
  1. in 2D, where the rectangle ABCD and the point V are in the same plane?
  2. in 3D, where the diagram represents a pyramid, with vertex V, on a rectangular base ABCD?

Published May 1998.