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

## IM Commentary

The objective of this job is because that students to articulate a an interpretation for a trapezoid. There are two completing definitions for "trapezoid":

The exclusive an interpretation of a trapezoid claims that a trapezoid has specifically one pair that opposite sides parallel.

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

Sometimes world say trapezoids "have one pair that opposite political parties parallel," which leaves it ambiguous even if it is there deserve to be an ext than one or not. The second component of the job pushes students to it is in clear about which variation they intend. Due to the fact that of the care students need to take through definitions, this job draws heavily on MP6, attend to precision.

After students have actually articulated definitions for us or v a partner, the course should discuss the meaning together. The class should decide on a single definition that they every agree on, together the suggest of having clearly articulated meanings is that us all understand we space talking about the very same thing. When both definitions are legitimate, the advantage to the inclusive definition is that any type of theorem verified true because that a trapezoid is likewise true for a parallelogram. Furthermore, in their study *The classification of quadrilateral * (Information period Publishing, 2008), Usiskin et al. Conclude,

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

Please watch the K-6 Geometry Progressions record for an ext information around 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 v one pair that opposite sides parallel. It deserve to have ideal angles (a ideal trapezoid), and it deserve to have congruent political parties (isosceles), however those are not required. Sometimes human being define trapezoids to have actually at least one pair of opposite political parties parallel, and also sometimes say there is one and also only one pair that opposite political parties parallel. The parallelogram fits the "at the very least one" variation of the meaning because it has two pairs of opposite sides parallel, thus it falls into the category of gift both a trapezoid and also a parallelogram. The parallelogram does not fit the "one and also only one" variation of the definition. So just how students answer this counts on your definition.Note: if college student come up with various definitions, that is well initially. However, in order to be able to discuss mathematical ideas going forward, the class should resolve on among these versions and go indigenous there. See keep in mind in the comment encouraging the version of the meaning that has parallelograms.