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The Theorem Of Pythagoras.

The Theorem Of Pythagoras. c. 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.

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The Theorem Of Pythagoras.

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  1. The Theorem Of Pythagoras. c • 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. b a

  2. Complete the results of your table below: 5 9 16 25 13 25 144 169 10 36 64 100 17 64 225 289 By considering all the numbers in the completed table can you see what Pythagoras discovered ? The Theorem Of Pythagoras: a2 + b2 = c2

  3. Calculating An Unknown Side. • The longest side of a right angled triangle is called the hypotenuse. HYPOTENUSE c a • Pythagoras discovered that the sum of the squares of the two shorter sides is equal to the square of the hypotenuse. b a2 c2 + b2 =

  4. Find the side A in this triangle. A 6 8 Hint Follow this routine exactly every time to solve Pythagoras problems easily. Solution. A2 = 82 + 62 A2 = 64 + 36 A2= 100 A = √100 A =10

  5. W 6.4cm 5.8cm What Goes In The Box? Find the length of side W in this right angled triangle. W2 + 5.82 = 6.42 = W2 40.96 + 33.64 W2 = 74.6 W = 74.6 W = 8.6cm

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

  7. Finding A Shorter Side. Calculate the length of side W. W2 + 12.32 = 14.7 2 14.7m W2 + 151.29 = 216.09 W2 = 216.09 – 151.29 W W = √ 64.8 W = 8.05 m 12.3m

  8. 3.4m 2.6m H Find the length of side H in the right angled triangle below: What Goes In The Box? 2 + 2.62 = 3.42 H2 6.76 = 11.56 H2 + - 6.76 H2 = 11.56 H2 = 4.8 H = 4.8 H = 2.19m

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

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