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.
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