Yes
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A polygon is a 2 dimensional shape with three or more sides that is closed in. A trapezoid is a four sided shape with only one pair of parallel sides. Therefore all trapezoids are polygons.
No trapezoids are parallelograms, and no parallelograms are trapezoids.
There are isosceles trapezoids which are sometimes called regular trapezoids.
NO rectangles are trapezoids
Trapezoids always have 4 sides, and 1 set of parallel lines.