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The goal of this task is to provide an opportunity for students to apply a wide range of ideas from geometry and algebra in order to show that a given quadrilateral is a rectangle. Creativity will be essential here as the only given information is the Cartesian coordinates of the quadrilateral's vertices.

This lesson unit is intended to help you assess how well students understand the relationship between the slopes of parallel and perpendicular lines and in particular, to help identify students who find it difficult to:
Find, from their equations, lines that are parallel and perpendicular.
Identify and use intercepts.
It also aims to encourage discussion on some common misconceptions about equations of lines.

In this task, you are given four points on a graph, and must prove that they are the corners of a square.

This discovery lesson has students determine slopes of a series of lines and then pairing them as parallel, perpendicular or neither.  Once they are paired, students have to determine how they know that lines are perpendicular.

The goal of this task is to use similar triangles to establish the slope criterion for perpendicular lines. Students need to be familiar with scaling and with the side-side-side congruence criterion.

The goal of this task is to examine when two lines in the plane are perpendicular in terms of their slopes.