You are watching: A quadrilateral with only one set of parallel sides

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

## IM Commentary

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

The exclusive definition of a trapezoid claims that a trapezoid has exactly one pair of opposite sides parallel.

The inclusive definition states the a trapezoid has at least one pair the opposite political parties parallel.

Sometimes people 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 component of the task pushes college student to it is in clear about which version they intend. Due to the fact that of the care students must take through definitions, this task draws greatly on MP6, address precision.

After students have articulated meanings for us or through a partner, the course should comment on the definition together. The course should decide on a single an interpretation that they every agree on, as the suggest of having clearly articulated interpretations is that we all understand we room talking about the exact same thing. If both interpretations are legitimate, the advantage to the inclusive meaning is that any theorem showed true because that a trapezoid is likewise true because that a parallelogram. Furthermore, in their research *The category of quadrilateral * (Information age Publishing, 2008), Usiskin et al. Conclude,

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

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

See more: What Does Kia Mean In Japanese, Kia Translation Into Japanese

## Solution

A trapezoid is a quadrilateral with one pair that opposite political parties parallel. It have the right to have right angles (a appropriate trapezoid), and it deserve to have congruent political parties (isosceles), yet those room not required. Sometimes human being define trapezoids to have at the very least one pair the opposite sides parallel, and sometimes say there is one and only one pair the opposite political parties parallel. The parallel fits the "at least one" version of the an interpretation because it has actually two pairs of opposite sides parallel, as such it drops 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 how students answer this relies on their definition.Note: if college student come up with various definitions, that is fine initially. However, in bespeak to be able to discuss mathematical concepts going forward, the class should settle on among these versions and also go indigenous there. See keep in mind in the comment encouraging the version of the meaning that includes parallelograms.