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Is this parallel a trapezoid according to your definition? Explain.

## IM Commentary

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

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

The inclusive an interpretation states that a trapezoid contends least one pair that opposite sides parallel.

Sometimes world say trapezoids "have one pair the opposite political parties parallel," which leaves it ambiguous even if it is there can be more than one or not. The second component of the task pushes student to be clear about which version they intend. Since of the treatment students should take v definitions, this task draws greatly on MP6, attend to precision.

After students have articulated definitions for us or through a partner, the course should discuss the meaning together. The course should decide on a single definition that they all agree on, together the suggest of having clearly articulated definitions is that us all understand we room talking around the exact same thing. When both interpretations are legitimate, the benefit to the inclusive meaning is that any theorem showed true for a trapezoid is likewise true for a parallelogram. Furthermore, in their research *The classification of quadrilateral * (Information period Publishing, 2008), Usiskin et al. Conclude,

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

Please see the K-6 Geometry Progressions paper for an ext 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 the opposite political parties parallel. It deserve to have ideal angles (a appropriate trapezoid), and also it have the right to have congruent sides (isosceles), however those room not required. Sometimes human being define trapezoids to have at least one pair of opposite political parties parallel, and also sometimes say there is one and only one pair that opposite political parties parallel. The parallel fits the "at least one" variation of the definition because it has two pairs of opposite political parties parallel, therefore it falls into the category of gift both a trapezoid and a parallelogram. The parallelogram does no fit the "one and also only one" variation of the definition. So exactly how students prize this depends on their definition.Note: if college student come up with different definitions, the is fine initially. However, in bespeak to have the ability to discuss mathematical ideas going forward, the course should clear up on one of these versions and also go native there. See keep in mind in the commentary encouraging the version of the meaning that includes parallelograms.