You get a bonus - 1 coin for daily activity. Now you have 1 coin

Rectangular parallelepiped. Property

Lecture



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:

  Rectangular parallelepiped.  Property

From the right triangle ACB by the Pythagorean theorem we get

  Rectangular parallelepiped.  Property

The edges AB, BC and CC `are not parallel, and therefore their lengths are linear dimensions of the parallelepiped. The theorem is proved.
created: 2014-10-05
updated: 2021-03-13
132539



Rating 9 of 10. count vote: 2
Are you satisfied?:



Comments


To leave a comment
If you have any suggestion, idea, thanks or comment, feel free to write. We really value feedback and are glad to hear your opinion.
To reply

Stereometry

Terms: Stereometry