Trapezoid is not parallelogram and parallelogram is not trapezoid.
A trapezoid (in North America) or a trapezium (in Britain and elsewhere) is a quadrilateral (a closed plane shape with four linear sides) that has at least one pair of parallel lines for sides. Some authors define it as a quadrilateral having exactly one pair of parallel sides
In North America, the term trapezium is used to refer to a quadrilateral with no parallel sides. The term trapezoid was once defined as a quadrilateral without any parallel sides in Britain and elsewhere, but this usage is now obsolete. A trapezoid with vertices ABCD would be denoted as ABCD.