Pythagoras Pythagoras of Samos lived from about 569

Pythagoras

Pythagoras of Samos lived from about 569 BC to about 475 BC Pythagoras was a Greek philosopher who made important developments in mathematics, astronomy, and theory of music The theorem now known as the Pythagoras theorem was known before the time of Pythagoras (about 2500 years ago. ) The Egyptians used it in one form, and a Chinese scholar Tschou-Gun knew the form of it 3000 years ago. Pythagoras generalised the relationship and made what is possibly the first proof. After Pythagoras, it became well known, consequently he was given the credit for it.

Lesson Objective To understand theory and practicalities of Pythagoras’ Theorem Lesson Success Criteria • Can understand how to derive the Pythagoras’ Theorem • Can use Pythagoras’ Theorem in solving problems

Introduction You have heard of the Pythagorean Theorem, and you know that it can be used to find the missing side of a right triangle. But does it always work? Why? And is there any use for it in real life? (Other than the fact that it keeps showing up on pesky exams!)

Pythagoras Theorem NOTE: - ‘h’ is always opposite the right angle - it doesn’t matter which of the two sides you label ‘a’ and ‘b’ - Pythagoras only relates to the lengths of a right-angled Δ

PROOFS There are currently well over a hundred different proofs for the Pythagoras theorem. One of the most common ones is that showing the combination of areas of the two smallest sides equaling the area of the longest side

PROOF – using similar triangles ΔACB similar to ΔAHC similar to ΔBHC - all share angle θ and a ⦜

What can we use Pythagoras for?

Practical Problems

Practical Problems Baseball You've just picked up a ground ball at first base, and you see the other team's player running towards third base. How far do you have to throw the ball to get it from first base to third base, and throw the runner out?

Practical Problems What is the longest length of a nail that could fit inside this cuboid object that measures 10 cm by 3 cm by 2 cm?

Skills check 1) What is the algebraic equation for the Pythagorean Theorem? 2) What does the Pythagorean Theorem allow you to do? 3) When can you use the Pythagorean Theorem?

Practice From homework book Page 215: Ex K: Finding hypotenuse Page 217: Ex L: Finding other sides Page 219: Ex M: Pythagoras applications