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

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

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IM Commentary

The purpose of this job is for students to articulate a definition for a trapezoid. There room two completing definitions because that "trapezoid":

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

The inclusive definition states the a trapezoid contends least one pair of opposite political parties parallel.

Sometimes human being say trapezoids "have one pair that opposite political parties parallel," which leaves it ambiguous whether 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 around which variation they intend. Since of the care students have to take v definitions, this job draws heavily on MP6, attend to precision.

After students have actually articulated meanings for us or v a partner, the class should talk about the meaning together. The course should decision on a single an interpretation that they every agree on, as the suggest of having clearly articulated definitions is that we all recognize we are talking about the same thing. When both meanings are legitimate, the advantage to the inclusive definition is that any theorem proved true for a trapezoid is additionally true because that a parallelogram. Furthermore, in their examine The classification of quadrilateral (Information age Publishing, 2008), Usiskin et al. Conclude,

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

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

Please view the K-6 Geometry Progressions file for much more information about these issues: http://commoncoretools.me/wp-content/uploads/2012/06/ccss_progression_g_k6_2012_06_27.pdf.

See more: What Symbol On An Ordnance Survey Map Denotes A Golf Course? ?


Solution

A trapezoid is a quadrilateral through one pair the opposite sides parallel. It can have appropriate angles (a ideal trapezoid), and it have the right to have congruent sides (isosceles), however those are not required. Sometimes civilization define trapezoids to have actually at least one pair of opposite political parties parallel, and sometimes say there is one and only one pair that opposite political parties parallel. The parallel fits the "at the very least one" version of the definition because it has two bag of opposite political parties parallel, as such it falls into the classification of gift both a trapezoid and a parallelogram. The parallel does no fit the "one and only one" version of the definition. So just how students answer this relies on their definition.

Note: if student come up with various definitions, the is well initially. However, in stimulate to have the ability to discuss mathematical principles going forward, the class should work out on among these versions and also go from there. See note in the comment encouraging the version of the definition that contains parallelograms.