It is a square or a rhombus. They are the only two equilateral parallelograms.
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No, all sides are UNEQUAL. Nope, all different. All sides equal would be equilateral which means "equal sides"
A parallelogram where all sides are equal is a square.
Not unless all angles are also equal. A rhombus is a parallelogram with all sides equal. A rectangle is a parallelogram with all angles equal. A square is a rhombus with all angles equal which is a parallelogram with all sides equal and all angles equal.
a rectangle
Square. By definition, its sides must all be equal.