No.
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A parallelogram
no, only a rhombus or square does, which is a special case of a parallelogram; in general, only two sides will be equal for a parallelogram.
The opposite sides are equal, so 2 pairs of equal sides, or in special circumstances where they are all equal, the answer is 4 (4 equal sides makes it a rhombus, which is a special parallelogram)
A rhombus.
A square is a rectangle with 4 equal sides and 4 equal angles. A rhombus is a parallelogram with 4 equal sides.