2. The Theorem Of Pythagoras Pythagoras was a Greek Mathematician.(580- 500B.C). 2500 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.

3. 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??? ?

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

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

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

7. Does this work for all right-angled triangles? abca2a2 b2b2 c2c2 34 512 68 8 15 591625 1325144169 3664100 17 64225289 10 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

8. 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

9. 6 (b) 8 (a) c Find the side ‘C’ (the hypotenuse) in this triangle. Solution. c 2 = 8 2 + 6 2 c 2 = 64 + 36 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

10. Find the unknown side in each of the triangles below. 9 (1) 8 A (2) 6 7 B (3) 23 9 C (4) 6.8 8.3 D (5) 8.9 22.7 E 12.04 9.22 24.7 10.73 24.38