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I recently came across this in my textbook:

Any three vertices of a cube determine a right triangle. Is this a true statment?

My initial thought was that is was, but the answers say otherwise. I cannot, however, come up with a counterexample.

What three vertices of a cube don't determine a right triangle?

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You are standing at a corner. Consider the three corners closest to you.

These three corners determine a triangle, all of whose sides are face diagonals. So all these sides have equal length, the triangle is equilateral.

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    Ah, I see! Thanks!2012-12-17
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Hint: Draw the cube so that it looks like a hexagon.

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    Ah, there it is! That is an interesting way to look at it! Thanks!2012-12-17
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Three that involve no edges from the cube. If the vertices are the standard ones for the unit cube, then, $(0,0,0)$, $(0,1,1)$, and $(1,1,0)$ will do.