Question: For the final assignment, all proofs are optional. 1. Prove the Pythagorean Theorem. That is, in a right triangle, with legs a and b,

For the final assignment, all proofs are optional. 1. Prove the Pythagorean Theorem. That is, in a right triangle, with legs a and b, and hypotenuse c, show that a + b = c. 2. Show that 3 is an irrational number. That is, show that 3 cannot be written in where a and b are both integers, and b 0. the form a b T 3. Show that, if 0

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