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A parallelogram is such a shape.
A parallelogram has two pairs of parallel sides.
A parallelogram has two pairs of opposite parallel sides
Yes it does. All the four sides have an opposite. The opposites are parallel so in a parallelogram there are two pairs of parallel sides.
I would be seriously concerned if a quadrilateral had more than two pairs of opposite sides parallel! A quadrilateral with two pairs of opposite sides parallel is a parallelogram.