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This is called a square or a rhombus. If the vertices of the four corners are all right angles, it is a square. Otherwise it is a rhombus.

Q: A polygon with 4 equal sides and two pairs of parallel sides?

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Not all polygon have two pairs of parallel sides. For example, a square will, but not a triangle.

An isosceles trapezoid has a pair of parallel sides and a pair of equal base angles

A rectangle perhaps?

Any polygon with more than 3 sides can have two pairs of parallel sides.If it has only four sides and they make two parallel pairs, then it's a parallelogram.

An irregular quadrilateral, though it could possibly be a kite if there are two pairs of sides of equal length

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Not all polygon have two pairs of parallel sides. For example, a square will, but not a triangle.

It depends on the actual shape of that octagon. It CAN have two pairs of parallel sides. A regular octagon has 4 pairs of parallel sides.

An isosceles trapezoid has a pair of parallel sides and a pair of equal base angles

A parallelogram has 2 pairs of parallel sides.

A rectangle perhaps?

A parallelogram, or variants of polygons with 6 or more sides.

quadrilateral

Any polygon with more than 3 sides can have two pairs of parallel sides.If it has only four sides and they make two parallel pairs, then it's a parallelogram.

A four sided polygon with two pairs of parallel sides is called a Parallelogram.

An isosceles triangle. It has two pairs of equal sides, which are also not parallel.

5 pairs of parallel sides.

An irregular quadrilateral, though it could possibly be a kite if there are two pairs of sides of equal length