No, a parallellogram has the same both "top" and "bottom" size. A trapezoid has diffrent both "top" and "bottom" size.
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parallellogram and rhombus
No, not every trapezoid is an isosceles trapezoid.
The altitude of a trapezoid bisects the bases of the trapezoid.
All the names to classify a trapezoid are a trapezoid and a quadrilateral.
A trapezoid can also take the form of an isosceles trapezoid