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# Pythagoras

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1. Pythagoras

2. History Pythagoras was a Greek mathematician who was born approximately 2700 years ago. He was responsible for figuring out a lot of modern maths, especially geometry and trigonometry.

3. Pythagoras came up with a rule to work out the sides of a right angled triangle. The rule only works for right angled triangles. To use the rule you need 2 sides.

4. The rule says that if you square each of the two short sides of a triangle then add them together it will equal the square of the long side. Short Long Short

5. c a b a2 + b2 = c2

6. long short short short2 + short2 = long2

7. To find the long side • Square both short sides • Add the squares together • Square-root your answer

8. 3 x 4 32 = 9 42 = 16 16 + 9 = 25 Square root of 25 = 5

9. 9 x 12 92= 81 122= 144 81 + 144 = 225 Square root of 225 = 15

10. To find a short side • Square the long side • Square the short side • Subtract the short square from the long square • Square-root your answer

11. a 20 16 202 = 400 162 = 256 400 - 256 = 144 Square root of 144 = 12

12. a 14 11 142= 196 112= 121 196- 121 = 75 Square root of 75 = 8.7 (1dp)

13. Recap (don’t copy) • Pythagoras's rule can be used to find the last side of a right angled triangle. • The first step is to square the sides. • Then: • if they are both short sides add them. • or take the short side away from the long. • Then square root your answer.

14. 4.5 x 6 4.52 = 20.25 62 = 36 20.25 + 36 = 56.25 Square root of 56.25 = 7.5

15. a 20 7 16 9 92 = 81 72 = 49 81 - 49 = 32 Square root of 32 = 5.7