(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(x2+y2+z2)=a2+b2+c2+d2+e2+f2 geometry3D geometrytetrahedronparallelogram