A quadrilateral with no parallel sides is commonly referred to as a trapezium in American English or a trapezoid in British English. This type of quadrilateral features four sides (or edges) and four angles, but unlike other quadrilaterals, it does not have any pair of sides that are parallel.
The absence of parallel sides means that all opposite angles and side lengths vary. This distinguishes trapeziums from other quadrilaterals like trapezoids (which have at least one pair of parallel sides), rectangles, and squares (which have two pairs of parallel sides). A trapezium can take on various shapes and can be classified further based on the lengths of its sides and angles, but the key characteristic remains the lack of parallelism.
To visualize, imagine a four-sided figure where no side runs alongside another side indefinitely. This creates a unique outline that can sometimes appear irregular or asymmetrical. Understanding quadrilaterals like trapeziums is essential in geometry as they help in exploring the properties and relations of shapes within the broader category of polygons.