Sometimes they are.
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Some parallelograms are squares - the ones which are equiangular (have equal angles) and are equilateral (have equal side lengths). All squares are parallelograms, but only some parallelograms are squares.
sometimes
Yes
Never, honey. Just because a parallelogram has those fancy opposite sides that are parallel, doesn't mean it automatically becomes a rectangle. Rectangles have those nice right angles, while parallelograms can be all slanted and sassy. So, keep those shapes in check, darling.
The moon.