# Trapezoids

In geometry, how many sides does a trapezoid have?

A trapezoid has four straight sides, but its exact shape depends on where you are in the world. For example, in the United States, a trapezoid has two sides that are parallel to each other, but in the United Kingdom, the word "trapezoid" refers to a 4-sided shape that doesn't have any parallel sides.

The classification of trapezoids is uniquely contested. Outside of the U.S. and Canada, a quadrilateral with at least one pair of parallel sides is called a trapezium, but the shape known by that name within the U.S. and Canada is defined as one with no parallel sides. Confused? Us too.

Euclid, the forefather of modern geometry, defines a square as having equal sides and right angles; an oblong to have four right angles (but not four equal sides); a rhombus to have four equal sides (but no right angles); and a rhomboid to have equal opposite sides and equal opposite angles (but without right angles and without four equal sides). All other quadrilaterals were classified as trapezia. Should be easy enough, right?

Wrong. Interestingly, according to the Oxford English Dictionary, the confusion of trapezium and trapezoid between the U.S. and U.K. dates back to an error in Hutton's Mathematical Dictionary in 1795, which directly reversed the accepted meanings. Hutton assigned trapezium to "no sides parallel" and trapezoid to "two sides parallel."

In the United States, the Hutton definitions became standard, while the Proclus definitions remained standard in England. Two hundred years later, the controversy remains. Country by country, region by region, and even school by school, the definitions of trapezoid and trapezium are often swapped.

And now, a geometry joke: