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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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Q: Which shapes have opposite sides congruent and parallel?
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What shapes have opposite angles congruent?

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


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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.


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