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Q: Quadrangle with no pairs of parellel sides?

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Not sure about "parellel" but a quadrangle with two pairs of parallel lines MUST be a parallelogram.

A quadrangle with two pairs of equal sides is a square.

A quadrangle (or quadrilateral) that has two pairs of parallel sides is called a parallelogram.

draw a quadrangle that has 2 pairs of equal sides but is not a parallelogram

Draw a quadrangle with two parallel sides

a rhombus

a parallelogram, a rhombus, a rectangle, and a square.

It is a parallelogram.

A kite.

A parallelogram.

A parallelogram

A quadrangle (or quadrilateral) has only four sides so it is not possible for one to have three pairs of parallel sides. Therefore, the question makes no sense.

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