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

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

## IM Commentary

The objective of this job is because that students come articulate a definition for a trapezoid. There are two contending definitions for "trapezoid":

The exclusive an interpretation of a trapezoid says that a trapezoid has precisely one pair that opposite political parties parallel.

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

Sometimes civilization say trapezoids "have one pair the opposite sides parallel," which pipeline it ambiguous even if it is there deserve to be more than one or not. The second component of the task pushes college student to be clear around which variation they intend. Since of the treatment students must take v definitions, this job draws greatly on MP6, resolve precision.

After students have actually articulated interpretations for us or through a partner, the course should discuss the meaning together. The course should decision on a single definition that they all agree on, together the suggest of having clearly articulated definitions is that we all know we are talking around the same thing. While both interpretations are legitimate, the benefit to the inclusive meaning is that any type of theorem proved true because that a trapezoid is also 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 in between parallelograms and trapezoids that is exactly analogous to to the relationship between squares and also rectangles; the meaning for rectangles has squares in the same means that the inclusive an interpretation of trapezoids contains parallelograms.

Please check out the K-6 Geometry Progressions record for more 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 v one pair of opposite sides parallel. It deserve to have best angles (a right trapezoid), and it can have congruent sides (isosceles), however those room not required. Sometimes world define trapezoids to have actually at least one pair of opposite sides parallel, and sometimes say there is one and also only one pair the opposite sides parallel. The parallelogram fits the "at least one" version of the an interpretation because it has two pairs of opposite sides parallel, because of this it falls into the classification of being both a trapezoid and also a parallelogram. The parallelogram does no fit the "one and only one" version of the definition. So how students price this depends on their definition.Note: if college student come up with different definitions, the is well initially. However, in stimulate to have the ability to discuss mathematical concepts going forward, the course should work out on one of these versions and also go from there. See keep in mind in the comment encouraging the version of the meaning that consists of parallelograms.