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IM Geometry Unit 3 Lesson 14

What do you notice? What do you wonder?

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Elena is playing with the equivalent ratios she wrote in the warm-up. She rewrites  . Diego notices and comments, “I got  . The  and remind me of the Pythagorean Theorem.” Elena says, “The Pythagorean Theorem says that  I bet we could figure out how to show that.”
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How did Elena get from to ?

What equivalent ratios of side lengths did Diego use to get ?

When Pythagoras proved his theorem he used the 2 images shown here.
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Can you figure out how he used these diagrams to prove  in a right triangle with hypotenuse length c?

IM G Unit 3 Lesson 1 from IM Geometry by Illustrative Mathematics, https://im.kendallhunt.com/HS/students/2/3/14/index.html. Licensed under the Creative Commons Attribution 4.0 license, https://creativecommons.org/licenses/by/4.0/.