Yes.
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Yes. A parallelogram has congruent opposite sides as well as congruent opposite angles.
every parallelogram
Only a parallelogram. You can technically say a square does as well, although all sides are congruent in a square (compared to the parallelogram with two sets of opposite sides congruent).
A rhombus
No, you need both pairs of opposite sides to be congruent (i.e. the same size) to be a parallelogram.