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A Quadrilateral Kite!
If a set of equal sides are adjacent, then the quadrilateral is a "kite" shape. If a set of equal sides are opposite, then the quadrilateral is a parallelogram.
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.
A General Quadrilateral
A rhombus is a parallelogram with all its sides equal in length but none of its internal angles are right angles. If both pairs of opposite sides are of equal but different lengths then the quadrilateral is a simple parallelogram.If the two pairs of adjacent sides are of equal but different lengths then the shape is called a kite.