yes because they both have the same amount of sides (4)
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No. A parallelogram is a special kind of quadrilateral.
A quadrilateral and a rectangle are the same so.............
It may be. A quadrilateral has four sides, but they need not be all the same length, nor parallel to each other. It's true that a parallelogram *is* a quadrilateral.
No, you need both pairs of opposite sides to be congruent (i.e. the same size) to be a parallelogram.
A shape that is a parallelogram but not a quadrilateral doesn't exist.