This lesson guides students through a proof of the converse of the Pythagorean Theorem. Then students have an opportunity to decide if a triangle with three given side lengths is or is not a right triangle.
Lesson overview
 9.1 Warmup: The Hands of a Clock (5 minutes)

9.2 Activity: Proving the Converse (15 minutes)
 Includes "Are you Ready for More?" extension problem
 9.3 Activity: Calculating Legs of Right Triangles (10 minutes)
 Lesson Synthesis
 9.4 Cooldown: Is It a Right Triangle? (5 minutes)
Learning goals:
 Determine whether a triangle with given side lengths is a right triangle using the converse of the Pythagorean Theorem.
 Generalize (orally) that if the side lengths of a triangle satisfy the equation \(a^2+b^2=c^2\) then the triangle must be a right triangle.
 Justify (orally) that a triangle with side lengths 3, 4, and 5 must be a right triangle.
Learning goals (student facing):

Let’s figure out if a triangle is a right triangle.
Learning targets (student facing):
 I can explain why it is true that if the side lengths of a triangle satisfy the equation \(a^2+b^2=c^2\) then it must be a right triangle.
 If I know the side lengths of a triangle, I can determine if it is a right triangle or not.
Glossary:
 Access the complete Grade 8 glossary.
Standards:
 This lesson builds towards the standard:CCSS.8.G.B.6MS.8.G.6
IM 6–8 Math was originally developed by Open Up Resources and authored by Illustrative Mathematics, and is copyright 20172019 by Open Up Resources. It is licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0). OUR's 6–8 Math Curriculum is available at https://openupresources.org/mathcurriculum/.
Adaptations and updates to IM 6–8 Math are copyright 2019 by Illustrative Mathematics, and are licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0).
Adaptations to add additional English language learner supports are copyright 2019 by Open Up Resources, and are licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0).
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