Possibly the most famous theorem in all of mathematics. Over 300 distinct proofs of this theorem exist, including one discovered in 1876 by future president James Garfield. [Unfortunately, his mathematical prowess did not protect him from the assassin’s bullet.]
I introduced the Pythagorean Theorem today in class. Here’s how I’ve taught it before:
- State the theorem. For every right triangle, the square of the hypotenuse is equal to the sum of the squares of the two legs (a.k.a. for a right triangle, ). Almost every student has seen it before, either in middle school, in algebra, or in engineering.
- Do some practice questions involving solving for the unknown hypotenuse.
- Do some practice questions involving solving for an unknown leg.
- Do some practice questions involving Pythagorean whole number triples, where you have to figure out the third number without knowing whether it’s a leg or hypotenuse.
- Introduce the Pythagorean Theorem converse and do some practice questions of figuring out whether a triangle is acute, right, obtuse, or nonexistent.
- Have students research a proof of the Pythagorean Theorem, come to an understanding of it by reading it and working out the pictures and/or algebra, then write up a mini-report. Here‘s the project description.
Anything vital (or just extremely cool) that I’m missing? How do you teach the Pythagorean Theorem?