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Q: What is a quadrilateral with two pairs of opposite sides that are equal and parallel and has four right angles?

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rhombus

It is not possible for a quadrilateral in Euclidean plane geometry to have no equal angles and still have its opposite sides parallel.It's possible for a quadrilateral to have no equal angles and two of its sides parallel (opposite ones, obviously; adjacent sides can't possibly be parallel). That would be a trapezoid.

quadrilateral

Yes, the opposite angles in a regular quadrilateral are equal.

rhombus. The rhombus is a quadrilateral with all sides equal in length. It is also a parallelogram, so opposite sides are parallel and equal in length, and opposite angles are equal.

A parallelogram is a quadrilateral with opposite sides parallel (and therefore opposite angles equal

All quadrilaterals apart from rectangles. Even parallelograms have adjacent angles that are not equal.

rectangle

A rectangle.

a square

a rhombus, a quadrilateral without right angle, a quadrilateral with equal opposite parallel sides but no right angles

A rhombus is a 4 equal sided quadrilateral with opposite parallel sides and equal opposite acute angles and equal opposite obtuse angles that all add up to 360 degrees.

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