In this lesson, students apply their work with perpendicular slopes to categorize triangles and quadrilaterals. 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 apply the Pythagorean Theorem to determine if a figure is equilateral, and then use these calculations to more precisely describe the quadrilateral. Students use similar reasoning to categorize a set of triangles and to craft arguments to describe whether a triangle is a right triangle or not (MP3).