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Equilateral parallelograms do exist. They are called squares and rhombi (plural of rhombus).

A square is an equilateral rectangle, with four right angles.

A rhombus (diamond shape) is a quadrilateral with all four sides equal. Its opposite sides are parallel and each pair of opposite angles are equal.

(A cruder way of describing it might be a square with twisted angles, or a skew square. Such as: )



A non-equilateral parallelogram would look like this



One term used to describe these is a rhomboid.

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Q: What is an equilateral parallelogram in geometry?
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