No. Parallelograms are never trapezoids because in order to be a parallelogram there has to be two sets of parallel sides. A trapezoid only has one set of parallel sides.
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No but all parallelograms are trapezoids
No, but all parallelograms are trapezoids.
No. All rhombi (rhombuses) are parallelograms but all parallelograms are not rhombi.
Yes. All squares are parallelograms but not all parallelograms are squares.