Say what a trapezoid is in your own words. Compare your meaning with a partner.

You are watching: Quadrilateral with only one set of parallel sides

Is this parallelogram a trapezoid follow to her definition? Explain.

## IM Commentary

The function of this job is for 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 exactly one pair of opposite sides parallel.

The inclusive meaning states that a trapezoid has at least one pair of opposite political parties parallel.

Sometimes human being say trapezoids "have one pair of opposite sides parallel," which leaves it ambiguous whether there deserve to be more than one or not. The second part of the task pushes students to be clear about which version they intend. Because of the care students must take with definitions, this job draws greatly on MP6, address precision.

After students have actually articulated definitions for themselves or v a partner, the class should discuss the meaning together. The class should decision on a single meaning that they every agree on, together the allude of having clearly articulated interpretations is that us all recognize we room talking about the very same thing. When both meanings are legitimate, the benefit to the inclusive an interpretation is that any type of theorem verified true for a trapezoid is likewise true for 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 meaning of trapezoid has caused every the posts we could find top top the subject, and also most college-bound geometry books, to donate the inclusive definition.

The inclusive an interpretation sets increase a relationship between parallelograms and trapezoids the is exactly analogous come to the relationship between squares and also rectangles; the an interpretation for rectangles has squares in the same method that the inclusive meaning of trapezoids has parallelograms.

## Solution

A trapezoid is a quadrilateral through one pair the opposite sides parallel. It have the right to have right angles (a right trapezoid), and also it have the right to have congruent sides (isosceles), but those room not required. Sometimes world define trapezoids to have at the very least one pair of opposite political parties parallel, and also sometimes say over there is one and only one pair of opposite sides parallel. The parallel fits the "at the very least one" version of the an interpretation because it has actually two bag of opposite political parties parallel, because of this it drops into the classification of gift both a trapezoid and a parallelogram. The parallel does not fit the "one and only one" version of the definition. So how students answer this counts on your definition.

Note: if students come increase with different definitions, the is fine initially. However, in order to be able to discuss mathematical concepts going forward, the course should work out on one of these versions and also go native there. See note in the comment encouraging the version of the definition that has parallelograms.