There is no such object. Every quadrilateral must have adjacent sides. In fact, every polygon MUST have adjacent sides.
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A quadrilateral with congruent pairs of adjacent sides and no parallel sides is a kite.
A Quadrilateral Kite!
a kite (two pairs of adjacent congruent sides) or a trapezoid (one pair of parallel sides).
Two sides of a quadrilateral can be parallel.
It is not possible for a quadrilateral in Euclidean plane geometry to have no equal angles and still have its opposite sides parallel.It's possible for a quadrilateral to have no equal angles and two of its sides parallel (opposite ones, obviously; adjacent sides can't possibly be parallel). That would be a trapezoid.