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# Pythagoras Theorem Explained

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Pythagoras Theorem explained and then some worked examples and applications in Building and Screen Sizes.

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### Pythagoras Theorem Explained

1. 1. 54 3
2. 2. 5 4 3In Egypt, Pythagoras found out that they were using measurements with a Right Angled Triangle with sides of 3, 4, and 5 units to build the Pyramids. He decided to investigate this further.
3. 3. HypotenusePythagoras started with a 90 degree (L-shaped)Right Triangle. He named the long sloping sidethe “Hypotenuse”.
4. 4. 5 4 3Next he added a Square onto each Triangle Side.
5. 5. 5 4 3Next he added Grid Lines to measure Areas.
6. 6. C2 = 5 x 5 = 25A2 = 4 x 4 = 16 5 4 3 B2 = 3 x 3 = 9 He found that the Areas of the two side squares add up to equal the Area of the long sloping “Hypotenuse” square. Eg. 16 + 9 = 25
7. 7. 54 5 13 3 12 X28 10 17 8 6 15Pythagoras rule works on all Right Angled Triangles
8. 8. c = “Hypotenuse” Sloping Sidea = Altitude a2 + b2 = c2 b = Bottom Base a2 + b2 = c2a=6 6 10 c = 10 62 + 82 = 102 8 36 + 64 = 100 b=8 100 = 100 This 6,8,10 Right Triangle obeys Pythagoras Rule.
9. 9. Pythagoras Rule has been used since the days ofthe Pyramids to the present. Triangular shapes addstrength and rigidity to buildings and bridges.
10. 10. Pythagoras Rule is used in TVs and Projectors, as well asfor Phone and Computer screens in the form of 4:3 and16:9 viewing aspect ratios. The size of the screen ismeasured as the Diagonal of the right triangle.