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Is this parallelogram a trapezoid follow to your definition? Explain.

## IM Commentary

The objective of this task is because that students to articulate a an interpretation for a trapezoid. There space two contending definitions because that "trapezoid":

The exclusive definition of a trapezoid claims that a trapezoid has exactly one pair of opposite sides parallel.

The inclusive definition states the a trapezoid has at least one pair that opposite political parties parallel.

Sometimes people say trapezoids "have one pair that opposite sides parallel," which leaves it ambiguous even if it is there deserve to be more than one or not. The second component of the task pushes college student to be clear about which version they intend. Since of the treatment students should take through definitions, this task draws heavily on MP6, attend to precision.

After students have articulated meanings for themselves or with a partner, the class should talk about the definition together. The class should decide on a single an interpretation that they every agree on, together the allude of having clearly articulated interpretations is that us all understand we room talking about the exact same thing. If both interpretations are legitimate, the benefit to the inclusive definition is that any kind of theorem proved true for a trapezoid is likewise true because that a parallelogram. Furthermore, in their research *The group of square * (Information period Publishing, 2008), Usiskin et al. Conclude,

The inclusive an interpretation sets up a relationship between parallelograms and trapezoids that is specifically analogous come to the relationship in between squares and rectangles; the an interpretation for rectangles includes squares in the same way that the inclusive an interpretation of trapezoids includes parallelograms.

Please watch the K-6 Geometry Progressions file for much more information about these issues: http://commoncoretools.me/wp-content/uploads/2012/06/ccss_progression_g_k6_2012_06_27.pdf.

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## Solution

A trapezoid is a quadrilateral through one pair that opposite political parties parallel. It can have best angles (a best trapezoid), and also it deserve to have congruent political parties (isosceles), but those room not required. Sometimes world define trapezoids to have at the very least one pair that opposite sides parallel, and also sometimes say over there is one and also only one pair of opposite sides parallel. The parallel fits the "at the very least one" variation of the an interpretation because it has actually two bag of opposite political parties parallel, therefore it drops into the group of being both a trapezoid and also a parallelogram. The parallel does no fit the "one and only one" version of the definition. So just how students answer this counts on their definition.Note: if college student come increase with various definitions, that is good initially. However, in bespeak to have the ability to discuss mathematical concepts going forward, the course should clear up on among these versions and go from there. See keep in mind in the commentary encouraging the variation of the an interpretation that consists of parallelograms.