Say what a trapezoid is in your own words. Compare your definition with a partner.

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

## IM Commentary

The function of this job is for students to articulate a definition for a trapezoid. There are two completing definitions for "trapezoid":

The exclusive meaning of a trapezoid says that a trapezoid has exactly one pair of opposite political parties parallel.

The inclusive an interpretation states the a trapezoid has at least one pair of opposite political parties parallel.

Sometimes people say trapezoids "have one pair the opposite sides parallel," which leaves it ambiguous even if it is there deserve to be much more than one or not. The second part of the task pushes students to it is in clear about which variation they intend. Since of the treatment students need to take with definitions, this job draws greatly on MP6, deal with precision.

After students have actually articulated definitions for us or with a partner, the class should talk about the an interpretation together. The class should decide on a single an interpretation that they every agree on, together the suggest of having plainly articulated definitions is that us all know we space talking around the very same thing. When both interpretations are legitimate, the advantage to the inclusive meaning is that any theorem verified true because that a trapezoid is also true for a parallelogram. Furthermore, in their examine The category of quadrilateral (Information age Publishing, 2008), Usiskin et al. Conclude,

The preponderance of advantages to the inclusive definition of trapezoid has caused all the posts we could find top top the subject, and most college-bound geometry books, to favor the inclusive definition.

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

Please see the K-6 Geometry Progressions file for much more 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 through one pair the opposite sides parallel. It can have best angles (a best trapezoid), and it deserve to have congruent sides (isosceles), however those room not required. Sometimes civilization define trapezoids to have actually at least one pair the opposite sides parallel, and also sometimes say over there is one and also only one pair that opposite political parties parallel. The parallel fits the "at the very least one" version of the an interpretation because it has actually two pairs of opposite political parties parallel, thus it drops into the group of being both a trapezoid and a parallelogram. The parallel does no fit the "one and also only one" version of the definition. So exactly how students prize this counts on your definition.

Note: if students come increase with various definitions, the is fine initially. However, in bespeak to have the ability to discuss mathematical concepts going forward, the course should clear up on among these versions and also go indigenous there. See keep in mind in the comment encouraging the version of the meaning that consists of parallelograms.