A quadrilateral is a parallelogram if it has two pairs of parallel sides.
A quadrilateral is a trapezoid if it has one pair of parallel sides.
This implies that all parallelogram are trapezoid: if you have two pairs of parallel sides, you have one pair of parallel sides - you actually have more than required.
On the other hand, not all trapezoid are parallelogram: if you have one pair of parallel sides, you can't be sure that the other pair of sides will be parallel, too.
So, a trapezoid is not a parallelogram if it has only one pair of parallel sides, and the other two are not parallel.
