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the three special quadrilaterals that can be a parallelogram are a rectangle, a square, and a rhombus

Actually, this is incorrect.

All squares are rectangles. All rectangles are parallelograms. Therefore all squares are parallelograms.

But not all parallelograms are rectangles. And not all rectangles are squares.

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Q: Can a parallelogram be a rectangle and a square?
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Can a square or rectangle be a parallelogram?

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