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

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 preponderance of benefits to the inclusive definition of trapezoid has caused every the articles we can find top top the subject, and also most college-bound geometry books, to donate the inclusive definition.

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.