# Clip 10/24: Quadrilateral Closure - Part A

## Overview

Cathy Humphreys closes day one of the Properties of Quadrilaterals lesson. The second part of the investigation is getting students to justify and prove their findings about the diagonals of the kites. The students use definitions, postulates, and theorems to develop a proof about the diagonals of a quadrilateral and how they constrain the type of figure that is formed. The teacher moves between groups, checking in on the progress students are making in developing their justifications. At the close of the first period, the teacher employs the resource manager to make sure all the manipulatives and materials are collected and stored.

COMMENTARY BY COACH DAVID FOSTER: Cathy uses the phrase “convince yourself, convince a friend, convince a skeptic” to describe for students the level of precision necessary to justify findings.

The students were very successful at proving that if the diagonals are congruent and are perpendicular bisectors of each other, then the quadrilateral formed is a square.

Cathy checks in with each group, assessing where the students are in their thinking and how they are progressing in generating proofs. She finds a question to pose or re-directs the work around a specific task to move the group along.

Cathy makes group use of the group roles and the students respond positively by carrying out the duties assigned.