A parallelogram
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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.
Squares, rectangles, parallelograms and rhombuses have 2 pairs of parallel sides. The trapezoid has only 1 pair of parallel sides.
A kite has two pairs of equal-length sides. If that is the question, then kite will satisfy it.
A rhombus, or a square if there is a 90o angle.
Both pairs of opposite sides need to be congruent (the same length).