compose a cuboid to pyramids

shahar

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(1) Can any cube can be divided to 3 the same volume pyramids like in the picture?
(2) I think that cuboid can't that isn't a cube can't be divide into 3 volume pyramids. Why? Or Why am I wrong?
 

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(1) Can any cube can be divided to 3 the same volume pyramids like in the picture?
(2) I think that cuboid can't that isn't a cube can't be divide into 3 volume pyramids. Why? Or Why am I wrong?

The pyramids obtained this way will not in general be congruent. But they will always have the same volume, which can be shown by methods like Euclid's. And their volume will be the same as any pyramid with the same base and height.
 
I still not undersand

Why the pyramid in this way not be cogeruent? There is a geometric reason to that? or I accept it as an axiom?
 
Why the pyramid in this way not be cogeruent? There is a geometric reason to that? or I accept it as an axiom?
A general cuboid will have three faces made of three rectangles. You should be able to visualize that if these "face-rectangles" are NOT congruent - then the resulting pyramids will be non-congruent.

In the special case, where this cuboid is a cube (faces are congruent squares) - the resulting pyramids will be congruent.
 
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