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Q: A polygon with opposite sides parallel and congruent?

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Any polygon with an even number of sides can have opposite sides that are congruent and parallel.

A four-sided polygon with opposite sides parallel and all sides congruent is a square.

a trapezoid

Any polygon with 2n sides (n integer) where opposite sides are parallel, will have its opposite angles congruent.

A rectangle is a quadrilateral with opposite sides parallel and congruent and four right angles. If all four sides are congruent, it is a square.

The Opposite Sides Parallel and Congruent Theorem states that if a quadrilateral has a pair of opposite sides that are parallel and congruent, then the quadrilateral is a parallelogram.

A square's opposite sides are parallel and all the sides are congruent.

Yes opposite sides are parallel and congruent

A square is a four-sided polygon with two congruent parallel sides.

No

A square or a rhombus

There are many such shapes. Any polygon with an even number of sides can have opposite sides that meet the above requirements.

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