IM Geometry Unit 3 Lesson 14
What do you notice?[br][br]What do you wonder?
Elena is playing with the equivalent ratios she wrote in the warm-up. She rewrites [math]\frac{a}{x}=\frac{c}{a}[/math] . [br]Diego notices and comments, “I got[br][math]b^2=yc[/math] . [br][br]The [math]a^2[/math] and [math]b^2[/math] remind me of the Pythagorean Theorem.” Elena says, “The Pythagorean Theorem says that [math]a^2+b^2=c^2[/math][br][br]I bet we could figure out how to show that.”
How did Elena get from [math]\frac{a}{x}[/math] to [math]a^2=xc[/math]?
What equivalent ratios of side lengths did Diego use to get [math]b^2=yc[/math]?
When Pythagoras proved his theorem he used the 2 images shown here.
Can you figure out how he used these diagrams to prove [math]a^2+b^2=c^2[/math] in a right triangle with hypotenuse length [i]c[/i]?
IM G Unit 3 Lesson 1 from IM Geometry by Illustrative Mathematics, [url=https://im.kendallhunt.com/HS/students/2/3/1/index.html]https://im.kendallhunt.com/HS/students/2/3/14/index.html[/url]. Licensed under the Creative Commons Attribution 4.0 license, [url=https://creativecommons.org/licenses/by/4.0/]https://creativecommons.org/licenses/by/4.0/[/url].