IM Geo.3.14 Lesson: Proving the Pythagorean Theorem
What do you notice? What do you wonder?
Elena is playing with the equivalent ratios she wrote in the warm-up.
She rewrites as . 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.” How did Elena get from to ?
What equivalent ratios of side lengths did Diego use to get c?
Prove in a right triangle with legs length and and hypotenuse length .
When Pythagoras proved his theorem he used the 2 images shown here. Can you figure out how he used these diagrams to prove in a right triangle with hypotenuse length ?
James Garfield, the 20th president, proved the Pythagorean Theorem in a different way.
How does this diagram prove the Pythagorean Theorem? 