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Q: What shapes have opposite sides congruent?

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

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

Of some shape, Yes. Of other shapes, No.

a trapeziod

In short, no. Similar shapes are shapes in which all corresponding angles congruent regardless of the length of the sides. Congruent shapes have congruent corresponding angles and corresponding sides. In effect congruent shapes is a special condition of similar shapes.

Of the quadrilaterals: a square, a rectangle, a parallelogram and a rhombus

this would be a rhombus. rhombuses are parallelograms (four-sided shapes with opposite sides parallel) that have all equal side lengths. squares are included as rhombuses.

rectangle

A parallelogram has two pairs of congruent sides, and the opposite sides are congruent.

Yes, the opposite sides of a parallelogram are congruent.

All regular shapes have congruent sides.

Opposite sides are parallel, Consecutive angles are supplementary, Opposite angles are congruent, Opposite sides are congruent (APEX)

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