Are parallelograms trapezoids? - Answers

There is disagreement among authors on this. It depends on your definition of a trapezoid. A parallelogram is defined as a quadrilateral with opposite sides parallel. A trapezoid is defined as either- a quadrilateral with at least one pair of parallel sides, or- a quadrilateral with exactly one pair of parallel sides.Therefore, if you go with the former definition, yes all parallelograms are trapezoids, because all parallelograms have at least one pair of parallel sides. If you use the latter definition, no.The "at least one" definition is consistent with the trapezoid's uses in higher math, such as the trapezoidal rule for approximating integrals.You can say, however, that all trapezoids are not parallelograms.