Q: What is a quadrilateral with opposite sides that are equal and parallel?

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They are equal and parallel.

Equal and parallel

rectangle

It is not possible for a quadrilateral in Euclidean plane geometry to have no equal angles and still have its opposite sides parallel.It's possible for a quadrilateral to have no equal angles and two of its sides parallel (opposite ones, obviously; adjacent sides can't possibly be parallel). That would be a trapezoid.

A square and a rhombus both have all sides equal and opposite sides parallel.

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They are equal and parallel.

Equal and parallel

A quadrilateral with opposite sides equal and parallel

rectangle

It is not possible for a quadrilateral in Euclidean plane geometry to have no equal angles and still have its opposite sides parallel.It's possible for a quadrilateral to have no equal angles and two of its sides parallel (opposite ones, obviously; adjacent sides can't possibly be parallel). That would be a trapezoid.

A square and a rhombus both have all sides equal and opposite sides parallel.

A Rectangle

A square or a rectangle

A parallelogram.

A parallelogram.

That quadrilateral is known as a 'parallelogram'.

rhombus. The rhombus is a quadrilateral with all sides equal in length. It is also a parallelogram, so opposite sides are parallel and equal in length, and opposite angles are equal.