trapezoid
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The quadrilateral with two pairs of parallel sides
There are two definitions for trapezoids. One defines them as a quadrilateral with at least two parallel lines, which would include parallelograms. The other strictly defines trapezoids as quadrilaterals with exactly two parallel lines.
what quadrilateral has exactly two perpendicular sides.
It is a trapezoid that has one pair of opposite parallel sides of different lengths whereas a parallelogram has two pairs of parallel sides.
this isn't possible, as having all sides be different lengths would prevent the sides from being parallel.