There is some disagreement whether parallelograms, which have two pairs of parallel sides, should be counted as trapezoids. 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. This article uses the inclusive definition and considers parallelograms as special cases of a trapezoid.
Believe it or not, there is no general agreement on the definition of a trapezoid. In B&B and the handout from Jacobs you got the Exclusive Definition.
Exclusive Definition of Trapezoid
A quadrilateral having two and only two sides parallel is called a trapezoid.
However, most mathematicians would probably define the concept with the Inclusive Definition.
Inclusive Definition of Trapezoid
A quadrilateral having at least two sides parallel is called a trapezoid.
The difference is that under the second definition parallelograms are trapezoids and under the first, they are not.
The advantage of the first definition is that it allows a verbal distinction between parallelograms and other quadrilaterals with some parallel sides. This seems to have been most important in earlier times. The advantage of the inclusive definition is that any theorem proved for trapezoids is automatically a theorem about parallelograms. This fits best with the nature of twentieth-century mathematics.
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