The Theorem Of Pythagoras Pythagoras was a Greek Mathematician.( B.C) years old is even older than your teacher. He was eccentric. (mad!!) Don’t mention √ 2 to him!! He discovered an amazing rule about right angled triangles.

Pythagoras’ Theorem says: The square on the longest side of the triangle is equal to the sum of the squares on the other two sides. HUH??? ?

What does it all mean? Draw squares on the three sides of the triangle.

The area of the smaller squares adds up to the area of the largest square. +=

This is called Pythagoras’ Theorem. Pythagoras’ Theorem c2c2 b2b2 a2a2 c 2 =a 2 +b 2 c b a

Does this work for all right-angled triangles? abca2a2 b2b2 c2c By considering all the numbers in the completed table you can see what Pythagoras discovered. The Theorem Of Pythagoras: a 2 + b 2 = c 2 This works for ALL right-angled triangles. a b c

Calculating An Unknown Side. The longest side of a right angled triangle is called the hypotenuse. a b c  Pythagoras discovered that the sum of the squares of the two shorter sides is equal to the square of the hypotenuse. c 2 =a 2 +b 2 HYPOTENUSE

6 (b) 8 (a) c Find the side ‘C’ (the hypotenuse) in this triangle. Solution. c 2 = c 2 = c 2 = 100 c = √ c =10 Hint: Follow this routine exactly every time, to solve Pythagoras problems easily. c 2 = a 2 + b 2 100

Find the unknown side in each of the triangles below. 9 (1) 8 A (2) 6 7 B (3) 23 9 C (4) D (5) E