Lesson 14
Coordinate Proof
Lesson Narrative
In this lesson, students use coordinates to make conjectures and prove simple geometric theorems algebraically. They begin with some informal reasoning in a “Which One Doesn’t Belong” prompt. In the next activity, students use slopes to classify a quadrilateral. Then, they use inductive reasoning to observe a pattern and make a conjecture which will be generalized in a subsequent unit. Students have an opportunity to attend to precision in mathematical language (MP6) as they write and refine their conjectures. At the end of the lesson, students critique each other’s reasoning (MP3) about properties of the quadrilaterals from the warmup.
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.
Learning Goals
Teacher Facing
 Prove simple geometric theorems algebraically using coordinates.
Student Facing
 Let’s use coordinates to prove theorems and to compute perimeter and area.
Required Materials
Required Preparation
Devices and index cards are required for the digital version of the Circular Logic task.
Learning Targets
Student Facing
 I can use coordinates of figures to prove geometric theorems.
CCSS Standards
Glossary Entries

opposite
Two numbers are opposites of each other if they are the same distance from 0 on the number line, but on opposite sides.
The opposite of 3 is 3 and the opposite of 5 is 5.

pointslope form
The form of an equation for a line with slope \(m\) through the point \((h,k)\). Pointslope form is usually written as \(yk = m(xh)\). It can also be written as \(y = k + m(xh)\).

reciprocal
If \(p\) is a rational number that is not zero, then the reciprocal of \(p\) is the number \(\frac{1}{p}\).