yes it is possibe for a quadrilateral to have no equal sides
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Two sides of a quadrilateral can be parallel.
If it doesn't have parallel sides, it's just classified as a quadrilateral.
The key is the object is quadrilateral with parallel sides. It is a parallelogram. It is also a rhombus.
a parallelogram is a quadrilateral with four parallel sides. a trapezoid is a quadrilateral with two parallel sides.
A Trapezium is a quadrilateral with no parallel sides.