Yes. A parallelogram has two pairs of parallel sides. If the corners are all right angles, then the parallelogram is a rectangle, and if all sides are of equal length, it is also a square. It's impossible to make a square or rectangle, without them having two pairs of parallel sides.
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No. Only some parallelograms are rectangles. But all rectangles are parallelograms.
Yes. All rectangles are also parallelograms, but not all parallelograms are rectangles.
All rectangles are parallelograms, so yes there are some.
Some parallelograms are rectangles; all rectangles are parallelograms.
No. Rectangles are parallelograms with all right angles, while parallelograms just have 2 sets of parallel lines.