Say what a trapezoid is in your very own words. To compare your an interpretation with a partner.

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

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IM Commentary

The function of this task is because that students come articulate a meaning for a trapezoid. There are two completing definitions because that "trapezoid":

The exclusive an interpretation of a trapezoid states that a trapezoid has exactly one pair the opposite political parties parallel.

The inclusive definition states that a trapezoid has at least one pair the opposite sides parallel.

Sometimes world say trapezoids "have one pair that opposite political parties parallel," which leaves it ambiguous even if it is there have the right to be an ext than one or not. The second part of the job pushes student to it is in clear about which variation they intend. Because of the treatment students have to take v definitions, this job draws greatly on MP6, attend to precision.

After students have articulated interpretations for themselves or v a partner, the course should discuss the an interpretation together. The course should decision on a single an interpretation that they all agree on, together the allude of having plainly articulated interpretations is that we all understand we space talking around the very same thing. If both definitions are legitimate, the advantage to the inclusive meaning is that any type of theorem showed true for a trapezoid is likewise true because that a parallelogram. Furthermore, in their study The category of square (Information period Publishing, 2008), Usiskin et al. Conclude,

The preponderance of benefits to the inclusive an interpretation of trapezoid has actually caused all the articles we could find on the subject, and most college-bound geometry books, to donate the inclusive definition.

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

Please see the K-6 Geometry Progressions document 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 v one pair the opposite sides parallel. It deserve to have right angles (a appropriate trapezoid), and also it deserve to have congruent sides (isosceles), yet those space not required. Sometimes human being define trapezoids to have actually at the very least one pair that opposite political parties parallel, and also sometimes say there is one and also only one pair the opposite sides parallel. The parallel fits the "at least one" variation of the meaning because it has actually two bag of opposite political parties parallel, as such it falls into the group of being both a trapezoid and a parallelogram. The parallelogram does not fit the "one and only one" version of the definition. So exactly how students answer this relies on your definition.

Note: if students come up with various definitions, that is fine initially. However, in stimulate to have the ability to discuss mathematical ideas going forward, the class should work out on one of these versions and also go indigenous there. See keep in mind in the comment encouraging the variation of the definition that includes parallelograms.