In this lesson, students apply their work with perpendicular slopes to make conjectures and prove simple geometric theorems algebraically. They use slope and distance arguments to describe the type of quadrilateral that a set of coordinates determine. Using slope, students determine whether or not adjacent sides are right angles and opposite sides are parallel. They also observe a pattern and make a conjecture, which will be generalized in a subsequent unit. Finally, students critique each other's reasoning about the properties of a set of quadrilaterals (MP3).

One of the activities in this lesson works best when each student has access to devices that can run the Desmos applet, because students will benefit from seeing the relationship in a dynamic way.