Which is a right triangle formed using a diagonal through the interior of the cube?

it's not just a cube, but the diagonal of any box. imagine sitting in a nice rectangular room. you probably don't have to imagine; you're in one right now.

let's consider the right triangles. we get one whenever two line segments meet at a right angle. starting with the floor, the corner is a right angle formed by the edges along the walls. the diagonal across the floor is the hypotenuse of that right triangle.

consider one corner that's the endpoint of the diagonal. the floor is perpendicular to the line from that corner straight up along the edge to the ceiling. so that edge is perpendicular to every line in the plane of the floor including the diagonal we just drew.

so we have another right angle, between the diagonal we drew and the floor to ceiling corner line. that makes another right triangle, whose hypotenuse is the diagonal of the room.

when we apply the pythagorean theorem to our three dimensional case, the diagonal of a room satisfies

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step-by-step explanation: