2. The Theorem Of Pythagoras.

3.  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.  By completing the table opposite you are going to make the discovery for yourself. a b c abca2a2 b2b2 c2c2 34 512 610 815

4. Complete the results of your table below: abca2a2 b2b2 c2c2 34 512 68 815 591625 1325144169 3664100 1764225289 10 By considering all the numbers in the completed table can you see what Pythagoras discovered ? The Theorem Of Pythagoras: a 2 + b 2 = c 2

5. Calculating An Unknown Side.  The longest side of a right angled triangle is called the hypotenuse. a b c a2a2 +b2b2 = c2c2 HYPOTENUSE  Pythagoras discovered that the sum of the squares of the two shorter sides is equal to the square of the hypotenuse.

6. 6 8 A Find the side A in this triangle. Solution. A 2 = 8 2 + 6 2 A 2 = 64 + 36 A 2 = 100 A = √ 100 A =10 Hint Follow this routine exactly every time to solve Pythagoras problems easily.

7. What Goes In The Box? Find the length of side W in this right angled triangle. W 6.4cm 5.8cm W2W2 =6.4 2 +5.8 2 W2W2 = 40.96+33.64 W2W2 =74.6 W=  74.6 W=8.6cm

8. 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

9. Finding A Shorter Side. 14.7m 12.3m W Calculate the length of side W. W 2 + 12.3 2 = 14.7 2 W 2 + 151.29 = 216.09 W 2 = 216.09 – 151.29 W = √ 64.8 W = 8.05 m

10. What Goes In The Box? 2 Find the length of side H in the right angled triangle below: H 3.4m 2.6m H2H2 +2.6 2 =3.4 2 H2H2 + 6.76=11.56 H2H2 = -6.76 H2H2 =4.8 H=  4.8 H=2.19m

11. Calculate the size of the shorter side in the following. 12.4cm (1) 8.3cm A (2) 14.4m 19.8m B (3) 11.2mm 6.7mm C (4) 35.7m 22.6m D (5) 14.7cm 8.6cm E 9.2cm 13.59m 9mm 27.6m 11.9cm