Can you do this geometry challenge?

If there's a square slice of cheese for a full-sized burger, you've shown how to cut it into five pieces that can be rearranged into two smaller, congruent squares for sliders. Can a square be cut into *four* pieces and rearranged into two smaller, congruent squares?

You are cheating Howie, you need to get out your compass and show how to get the midpoints.

This is in the Meno! Neato

obviously join the midpoint of all the sides, that makes a diagonal square that has exactly half the area

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