How would you answer these two test questions:
(1) What is the "best" name of this shape?
(2) T or F: A rectangle is a trapezoid.
If you answered "I don't know...am I in England or the U.S.?" for both, you get full credit.
First, some surprising history. In 300 B.C., Euclid essentially used the term trapezium (meaning "little table") as the name of any quadrilateral other than a rectangle, square, parallelogram, or rhombus.
Eight hundred years later, the Greek geometer Proclus refined Euclid's terminology: a trapezium was a quadrilateral that had two parallel sides and a trapezoid (meaning "resembling a table") was a quadrilateral with no parallel sides.
Then, in 1795, Charles Hutton, an English mathematician, wrote his tome Mathematical and Philosophical Dictionary. In it, Hutton made an error and reversed Proclus' two definitions for trapezium and trapezoid...an error that was unknowingly adopted and propagated by British and American mathematicians.
And now the twist! Somehow, the British have corrected the error and now use Proclus's definitions. However, the Americans continue to follow the tradition established by Hutton.
Thus, on the quiz above, the British would respond (1) Trapezium and (2) No, while the Americans would respond (1) Trapezoid and (2) Maybe Yes.
This last qualification is due to the "worlds" unresolved dilemma: Does a trapezoid have at least two parallel sides or exactly two parallel sides?
For a final interesting experience, Google the two terms trapezium and trapezoid...and look only at the images generated. Thus, since Google is always right, we know that....
Source: Adapted by J.M.'s question and C. Funk's 2107 Curious Word Origins, Sayings & Expressions, 1993, p. 497-498.