Take your pick: square, rectangle, rhombus or parallelogram which all have opposite parallel sides
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Only if it is a trapezoid (US usage) with one set of parallel sides, or a parallelogram with both sets of opposite sides parallel. The term quadrilateral only means that the shape has 4 sides.
a square
Trapezoid
parallelogram
Any quadrilateral with two sets of parallel sides is called a parallelogram.