MathDB

(a) Prove the parallelogram law that says that in a parallelogram the sum of the squares of the lengths of the four sides equals the sum of the squares of the lengths of the two diagonals. (b) The edges of a tetrahedron have lengths

a, b, c, d, e

and

f

. The three line segments connecting the centers of intersecting edges have lengths

x, y

and

z

. Prove that

4 (x^2 + y^2 + z^2) = a^2 + b^2 + c^2 + d^2 + e^2 + f^2

Problem Statement