Q: A four sided shape that has two pairs of sides the same length but no parallel lines?

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A kite (if it's a quadrilateral).

a squareof course

parallelogram

A regular octagon.

Square, Rectangle.

Related questions

A kite (if it's a quadrilateral).

If it has 2 pairs of parallel lines it is a parallelogram, if it is a quadrilateral. If there is not restrictions on the number of sides, then there are many answers

Square

a squareof course

parallelogram

A rectangle

A regular octagon.

None

parallelogram

A triangle

A hexagon.

No, one pair.