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A trapezoid is a quadrilateral which must have one pair of parallel sides. If the other pair of sides is also parallel then it is a parallelogram.
First, there is no such word as trapozoid: it is trapezoid although most of the world know it as a trapezium.Whereas a trapezium has one pair of parallel sides, a parallelogram has two pairs of parallel sides.
A parallelogram with a right angle is a rectangle.
A trapezoid is a four-sided figure with two opposite sides parallel. A rectangle (and also a parallelogram) is a trapezoid but BOTH pairs of opposite sides are parallel.
The fact that (a) it has all the properties of a trapezoid, and (b) it has some additional properties, which not all trapezoids have, namely the fact that both sets of opposite segments are parallel.