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No. There is no way you can cut one rectangle in half and only get one square. The other half would also have to be a square and this will only happen if the proportions are 1:2 and you cut the long sides.

There are infinitely many ways to cut a rectangle in half none of which result in new rectangles. Only if the rectangle has proportions 1:2 can cutting it in half make a square, in fact the result could be two squares, not one.

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Q: If you cut a rectangle in half does it make a square?
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