Yes.
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Parrallelogram, quadrilateral, square... PLEASE ADD
No not every quadrilateral can be a regular polygon.
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.
No, not every quadrilateral is a trapezoid, although a trapezoid is also a quadrilateral because it has four sides.
Improved Answer:-Yes every trapezoid is a quadrilateral because they have 4 sides