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I assume you mean bisecting (1) top-to-bottom, (2) side-to-side, (3) top-left-to-bottom-right, and (4) top-right-to-bottom-left. Actually, any straight line through the center bisects the square into two congruent (!) pieces. So there are an infinite number of ways to cut a square into two equal pieces. A very similar answer would apply if you are trying to cut the square into four equal pieces.

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Q: Are there only 4 ways of cutting a square into equal pieces?
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