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

You are watching: A quadrilateral with one pair of parallel sides

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

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IM Commentary

The purpose of this task is for students come articulate a meaning for a trapezoid. There room 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 has at least one pair the opposite political parties parallel.

Sometimes human being say trapezoids "have one pair of opposite sides parallel," which pipeline it ambiguous even if it is there deserve to be an ext than one or not. The second component of the task pushes students to be clear around which variation they intend. Since of the treatment students have to take through definitions, this job draws greatly on MP6, address precision.

After students have articulated meanings for themselves or with 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 point of having clearly articulated meanings is that us all understand we room talking around the same thing. If both interpretations are legitimate, the advantage to the inclusive an interpretation is that any type of theorem verified true because that a trapezoid is additionally true because that a parallelogram. Furthermore, in their examine The category of quadrilaterals (Information age Publishing, 2008), Usiskin et al. Conclude,

The preponderance of benefits to the inclusive an interpretation of trapezoid has actually caused all the write-ups we might find top top the subject, and also most college-bound geometry books, to donate the inclusive definition.

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

Please see 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 through one pair that opposite political parties parallel. It can have best angles (a best trapezoid), and also it can have congruent sides (isosceles), but those room not required. Sometimes people define trapezoids to have actually at the very least one pair the opposite political parties parallel, and also sometimes say over there is one and also only one pair the opposite political parties parallel. The parallel fits the "at least one" variation of the definition because it has actually two pairs of opposite sides parallel, as such it drops into the classification of gift both a trapezoid and a parallelogram. The parallelogram does not fit the "one and only one" variation of the definition. So exactly how students prize this depends on your definition.

Note: if college student come increase with different definitions, that is good initially. However, in bespeak to have the ability to discuss mathematical ideas going forward, the class should resolve on one of these versions and also go from there. See keep in mind in the commentary encouraging the version of the definition that consists of parallelograms.