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.
Lesson overview
 14.1 Warmup: Which One Doesn’t Belong: Coordinate Quadrilaterals (5 minutes)

14.2 Activity: Name This Quadrilateral (15 minutes)
 Includes "Are you Ready for More?" extension problem
 14.3 Activity: Circular Logic (15 minutes)
 Lesson Synthesis
 14.4 Cooldown: Name That Quadrilateral (5 minutes)
Learning goals:
 Prove simple geometric theorems algebraically using coordinates.
Learning goals (student facing):
 Let’s use coordinates to prove theorems and to compute perimeter and area.
Learning targets (student facing):
 I can use coordinates of figures to prove geometric theorems.
Required materials:
 Geometry toolkits
 Graph paper
Required preparation:
 Devices and index cards are required for the digital version of the Circular Logic task.
Standards:
 This lesson builds towards the standard: CCSS.HSGGPE.B.4MS.GGPE.4MO.G.GPE.B.3
IM Algebra 1, Geometry, Algebra 2 is copyright 2019 Illustrative Mathematics and licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0).
The Illustrative Mathematics name and logo are not subject to the Creative Commons license and may not be used without the prior and express written consent of Illustrative Mathematics.