There is considerable confusion over the definition of 'trapezoid' and 'trapezium' due to differences in the British and US versions. As you can see from the table below, the meanings of the two words are exactly reversed between the US and British interpretations.
British | USA | |
Trapezoid | A quadrilateral with no sides parallel | A quadrilateral with one pair of parallel sides |
Trapezium | A quadrilateral with one pair of parallel sides | A quadrilateral with no sides parallel |