A quadrilateral with no pairs of parallel sides is best described as a trapezium in some regions, especially in the UK, or a irregular quadrilateral in a broader sense. This type of quadrilateral does not have any sides that are parallel to each other, making it distinct from other types of quadrilaterals such as rectangles, squares, and trapezoids, which do possess at least one pair of parallel sides.
In geometry, quadrilaterals are classified based on their properties, such as the lengths of their sides and the measures of their angles. When we talk about trapezium in the British context, it refers specifically to the shape with four unequal sides and no parallel sides. Conversely, in American terminology, a trapezium refers to any four-sided figure that does not have any parallel sides — thus, synonymously representing an irregular quadrilateral.
Irregular quadrilaterals can take many forms, varying in the lengths of their sides and the angles between those sides, leading to diverse shapes and sizes. While they lack the symmetry and regularity of other quadrilateral types, their unique appearance can lend itself to various applications in art, architecture, and design.
In summary, the best term to describe a quadrilateral with no pairs of parallel sides is a trapezium in UK terminology or an irregular quadrilateral more generally, highlighting the diversity and complexity within the world of quadrilaterals.