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The quadrilaterals with exactly one pair of parallel sides are:
1. Trapezoid: A quadrilateral with one pair of parallel sides. The other two sides are nonparallel.
2. Isosceles trapezoid: A quadrilateral with one pair of parallel sides and both pairs of opposite sides equal in length.
3. Parallelogram: A quadrilateral with both pairs of opposite sides parallel and equal in length.
4. Rhombus: A parallelogram with all four sides equal in length.
5. Rectangle: A parallelogram with all four angles equal to 90 degrees.
Note: A square can also be included in this list as a special case of rectangle and rhombus where all sides are equal in length and all angles are right angles.