Definition notes

trapezoid (US) = trapezium (UK)

In Euclidean geometry, a convex quadrilateral with at least one pair of parallel sides is referred to as a trapezoid in American and Canadian English but as a trapezium in English outside North America.

exclusive and inclusive definitions

Some define a trapezoid as a quadrilateral having only one pair of parallel sides (the exclusive definition), thereby excluding parallelograms. Others define a trapezoid as a quadrilateral with at least one pair of parallel sides (the inclusive definition), making the parallelogram a special type of trapezoid.

The latter definition is consistent with its uses in higher mathematics such as calculus. The former definition would make such concepts as the trapezoidal approximation to a definite integral ill-defined. The inclusive definition is also advocated in the taxonomy of quadrilaterals.

Source
http://en.wikipedia.org/wiki/Trapezoid
Further Reading
What is the correct definition for a trapezoid?
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