A quadrilateral has four sides and four vertices but no sides need to be parallel although they can be.
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A quadrilateral with congruent pairs of adjacent sides and no parallel sides is a kite.
A rectangle.
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.
a trapezoid!
A parallelogram.