Not usually,
The correct spelling is "parallelogram" (quadrilateral with two sets of parallel sides).
A trapezium (most of the world) or a trapezoid (US).
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Not only can a rhombus be a parallelogram, it must be one. A rhombus is a quadrilateral which has two pairs of parallel lines. That makes it a parallelogram.
Yes. It has two pairs of parallel sides.
Yes, every trapezoid is a quadrilateral.
No. Every parallelogram is not a rectangle but every rectangle is a parallelogram.
No not every quadrilateral can be a regular polygon.
It is true that every trapezoid is a quadrilateral
Parellelogram
No, not every quadrilateral is a trapezoid, although a trapezoid is also a quadrilateral because it has four sides.