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Which definition of a trapezoid works best for the Common Core Standards? At least one or only one pair of parallel sides. This question is geared towards K-6.
This comes directly from the Progression Document on Geometry K-6:
Note that in the U.S., that the term “trapezoid” may have two different meanings. In their study The Classification of Quadrilaterals (Information Age Publishing, 2008), Usiskin et al. call these the exclusive and inclusive definitions:
T(E): a trapezoid is a quadrilateral with exactly one pair of parallel sides
T(I): a trapezoid is a quadrilateral with at least one pair of parallel sides.
These different meanings result in different classifications at the analytic level. According to T(E), a parallelogram is not a trapezoid; according to T(I), a parallelogram is a trapezoid.
Both definitions are legitimate. However, Usiskin et al. conclude, “The preponderance of advantages to the inclusive definition of trapezoid has caused all the articles we could find on the subject, and most college-bound geometry books, to favor the inclusive definition.”
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