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Since parallelograms are four sided figures where each pair of opposing sides are parallel, and squares are four sided figures with all sides and angels congruent, then anything which is a square must also be a parallelogram. The statement is therefore false.
A four sided polygon with four congruent sides is a rhombusA square.
A four sided figure with no parallel sides is a trapezium, but it is also an irregular four-sided polygon, tetragon, quadrilateral, or quadrangle.