You are watching: A trapezoid is always an example of a

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

## IM Commentary

The function of this job is for students come articulate a an interpretation for a trapezoid. There are two competing definitions for "trapezoid":

The exclusive definition of a trapezoid states 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 the opposite political parties parallel.

Sometimes people say trapezoids "have one pair the opposite political parties parallel," which pipeline it ambiguous whether there have the right to be much more than one or not. The second part of the task pushes student to it is in clear about which version they intend. Due to the fact that of the treatment students must take through definitions, this task draws heavily on MP6, resolve precision.

After students have articulated meanings for us or v a partner, the class should talk about the an interpretation together. The class should decision on a single an interpretation that they every agree on, as the suggest of having plainly articulated interpretations is that us all know we room talking about the exact same thing. When both meanings are legitimate, the advantage to the inclusive an interpretation is that any theorem confirmed true because that a trapezoid is likewise true because that a parallelogram. Furthermore, in their examine *The classification of quadrilaterals * (Information period Publishing, 2008), Usiskin et al. Conclude,

The inclusive meaning sets increase a relationship between parallelograms and trapezoids the is exactly analogous to to the relationship in between squares and rectangles; the meaning for rectangles consists of squares in the same method that the inclusive an interpretation of trapezoids contains parallelograms.

Please view the K-6 Geometry Progressions record for 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 with one pair the opposite sides parallel. It have the right to have ideal angles (a appropriate trapezoid), and also it can have congruent sides (isosceles), however those are not required. Sometimes people define trapezoids to have at least one pair of opposite political parties parallel, and also sometimes say there is one and only one pair of opposite sides parallel. The parallel fits the "at least one" variation of the meaning because it has two pairs of opposite political parties parallel, because of this it falls into the classification of gift both a trapezoid and also a parallelogram. The parallel does not fit the "one and only one" version of the definition. So how students price this counts on their definition.Note: if student come up with different definitions, that is good initially. However, in bespeak to be able to discuss mathematical principles going forward, the class should clear up on among these versions and go native there. See keep in mind in the commentary encouraging the variation of the definition that has parallelograms.