There are may posibilities.
If it is a 4-sided figure, then a parallelogram. But if it has only two equal sides, it cannot be a rhombus (or square, which is a special case of rhombus).
It could also be a pentagon with vertices at A=(0,0), B=(2,0), C=(3,1), D=(3,2) and E= (0,2). Then AB and ED are parallel (both to the x-axis), and AE and CD are parallel (both to the y-axis). Also, AB and AE are both 2 units long. In this configuration, the x-coordinate of C and D could take almost any value as long as it was the same for these two points.
Then there are hexagons, heptagons etc, etc that can satisfy the requirements.
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A square is a regular polygon with two sets of parallel sides. A parallelogram is an irregular polygon with one set of parallel sides. A rhombus is an irregular polygon with two sets of parallel sides. A rectangle is an irregular polygon with two sets of parallel sides. *Note - a regular polygon is a shape in which all sides are equal in length and all angles are equal in measurement.
Parallelogram
a square
Yes. A square has two sets of equal and parallel opposite sides. All four sides and all four angles (right angles) are equal.
Any regular polygon with an even number of sides will have opposite sides that are parallel. For quadrilaterals (4-sided shapes), a trapezoid has one set of opposite sides and a parallelogram (rectangle, square, rhombus) has both sets of opposite sides parallel.