• a trapezium (UK) or a trapezoid (US) is a quadrilateral
with at least one pair of parallel sides.
• Parallel sides are called bases.
• Non-parallel sides are called legs or lateral sides.
See definition notes below examples.
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.
What is the correct definition for a trapezoid?
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The inclusive definition is used throughout this site.