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Q: What is a four-sided polygon with opposite sides parallel and all sides congruent?

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

a trapezoid

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

A quadrilateral

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.

There is no particular name. It need not be a regular polygon - for example, consider a stretched hexagon.

No

A four sided polygon where the opposite sides are parallel to each other (they must also by congruent). This also makes the opposite angles congruent. __ /_/ Sort of like that.

A square or a rectangle

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

It cannot be a quadrilateral because if one pair of opposite sides are congruent and parallel, it is a parallelogram and so the other two sides are also (mutually) congruent and parallel. Any polygon with 5 or more sides will have an irregular form which satisfies these conditions.

A square or a rhombus

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