Rectangular parallelepiped. Property

Theorem

In a rectangular parallelepiped, the square of any diagonal is equal to the sum of the squares of its three dimensions.

Evidence

Consider a rectangular parallelepiped ABCDA`B`C`D`. By the Pythagorean theorem in the triangle AC`C we get:



From the right triangle ACB by the Pythagorean theorem we get



The edges AB, BC and CC `are not parallel, and therefore their lengths are linear dimensions of the parallelepiped. The theorem is proved.