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Just out of curiosity, I tried to find if it was possible to make a square/rectangle out of two isosceles triangles. Is it really impossible to do so? Moreover, can a square/rectangle be cut into two isosceles triangles.

Though after trying to draw some pictures it seems impossible, is there a formal proof for it?

Clearly, a right triangle with a $45^\circ$ angle is an exception, but for the rest?

This question is not from any textbook, so I don't know if it holds any importance.

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