Trapezoids can be difficult to teach as there are two existing definitions. The Common Core Geometry Progression indicates that the inclusive definition is the preferred definition for trapezoids.
This text comes directly from the K-6 Geometry Progression:
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.”
The K-6 Geometry Progression can be found here:
Check with your state regarding which definition your state prefers. Georgia is using the inclusive definition. I looked on the Smarter Balanced and the PARCC websites and was unable to identify any information about which definition they prefer.
Currently I teach the exclusive definition of trapezoids to 3rd graders as their minds are already blown when they find out that squares are rectangles and rhombi. I expand the definition with 4th graders and teach them the inclusive definition. You may want to devise a vertical plan within your school on how to address this issue.
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