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Pythagoras' Theorem © Victoria Smith Begin. Right Angled Triangles Pythagoras’ Theorum will only work on a right angled triangle. ac b The longest side,

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Presentation on theme: "Pythagoras' Theorem © Victoria Smith Begin. Right Angled Triangles Pythagoras’ Theorum will only work on a right angled triangle. ac b The longest side,"— Presentation transcript:

1 Pythagoras' Theorem © Victoria Smith Begin

2 Right Angled Triangles Pythagoras’ Theorum will only work on a right angled triangle. ac b The longest side, opposite the right angle is the hypotenuse. Formula © Victoria Smith

3 Formula ac b a 2 + b 2 = c 2 Alternatively a 2 = c 2 - b 2 orb 2 = c 2 - a 2 Examples © Victoria Smith

4 Easy Examples x 3 4 x 2 = 3 2 + 4 2 Next © Victoria Smith

5 Easy Examples x 3 4 x 2 = 3 2 + 4 2 x 2 = 9 + 16 Next © Victoria Smith

6 Easy Examples x 3 4 x 2 = 3 2 + 4 2 x 2 = 9 + 16 x 2 = 25 Next © Victoria Smith

7 Easy Examples x 3 4 x 2 = 3 2 + 4 2 x 2 = 9 + 16 x 2 = 25 x = 5 Next © Victoria Smith

8 Easy Examples x 3 4 x 2 = 3 2 + 4 2 x 2 = 9 + 16 x 2 = 25 x =5 x 6 8 x 2 = 6 2 + 8 2 Next © Victoria Smith

9 Easy Examples x 3 4 x 2 = 3 2 + 4 2 x 2 = 9 + 16 x 2 = 25 x = 5 x 6 8 x 2 = 6 2 + 8 2 x 2 = 36 + 64 Next © Victoria Smith

10 Easy Examples x 3 4 x 2 = 3 2 + 4 2 x 2 = 9 + 16 x 2 = 25 x = 5 x 6 8 x 2 = 6 2 + 8 2 x 2 = 36 + 64 x 2 = 100 Next © Victoria Smith

11 Easy Examples x 3 4 x 2 = 3 2 + 4 2 x 2 = 9 + 16 x 2 = 25 x = 5 x 6 8 x 2 = 6 2 + 8 2 x 2 = 36 + 64 x 2 = 100 x = 10 Harder © Victoria Smith

12 Harder Example x 7 24 x 2 = 7 2 + 24 2 Next © Victoria Smith

13 Harder Example x 7 24 x 2 = 7 2 + 24 2 x 2 = 49 + 576 Next © Victoria Smith

14 Harder Example x 7 24 x 2 = 7 2 + 24 2 x 2 = 49 + 576 x 2 = 625 Next © Victoria Smith

15 Harder Example x 7 24 x 2 = 7 2 + 24 2 x 2 = 49 + 576 x 2 = 625 x = 25 Next © Victoria Smith

16 Harder Example x 7 24 x 2 = 7 2 + 24 2 x 2 = 49 + 576 x 2 = 625 x = 25 What happens if x is not the hypotenuse? Continue © Victoria Smith

17 Rearranging the Formula If x is not assigned the hypotenuse, you will need to rearrange the formula: 11 18 x 11 2 = 18 2 + x 2 Next © Victoria Smith

18 Rearranging the Formula If x is not assigned the hypotenuse, you will need to rearrange the formula: 11 18 x 11 2 = 18 2 + x 2 x 2 = 18 2 - 11 2 Next © Victoria Smith

19 Rearranging the Formula If x is not assigned the hypotenuse, you will need to rearrange the formula: 11 18 x 11 2 = 18 2 + x 2 x 2 = 18 2 - 11 2 x 2 = 324 - 121 Next © Victoria Smith

20 Rearranging the Formula If x is not assigned the hypotenuse, you will need to rearrange the formula: 11 18 x 11 2 = 18 2 + x 2 x 2 = 18 2 - 11 2 x 2 = 324 - 121 x 2 = 203 Next © Victoria Smith

21 Rearranging the Formula If x is not assigned the hypotenuse, you will need to rearrange the formula: 11 18 x 11 2 = 18 2 + x 2 x 2 = 18 2 - 11 2 x 2 = 324 - 121 x 2 = 203 x= 14.24 Summary © Victoria Smith

22 Summary Only works on right angled triangles The formula is a 2 + b 2 = c 2 If the side you are looking for is not the hypotenuse, you must rearrange the formula © Victoria Smith

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