A kite, and various options amongst polygons with 5 or more sides.
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a parelelogram
A square.
A parallelogram and selected polygons with 6 or more sides.
Yes. A parallelogram has two pairs of opposite sides parallel (and each pair of equal length). A rhombus has two pairs of opposite sides parallel (and each of those pairs of opposite sides are of equal length), thus it is a parallelogram. It is a special case of parallelogram where all four sides are equal in length, not just the opposite pairs.
A kite has two pairs of equal-length sides. If that is the question, then kite will satisfy it.