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The Theorem of Pythagoras

The Theorem of Pythagoras. How to label and name a right angled triangle. The 90 0 angle is the largest angle. The largest side is opposite the largest angle. The largest side is called the ‘HYPOTENUSE’. The Theorem of Pythagoras. Capital letters are used for angles.

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The Theorem of Pythagoras

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  1. The Theorem of Pythagoras How to label and name a right angled triangle. The 900 angle is the largest angle. The largest side is opposite the largest angle. The largest side is called the ‘HYPOTENUSE’.

  2. The Theorem of Pythagoras Capital letters are used for angles. The sides opposite the angles are given lower case letters. B a C A

  3. The Theorem of Pythagoras Capital letters are used for angles. The sides opposite the angles are given lower case letters. B a C b A

  4. The Theorem of Pythagoras Capital letters are used for angles. The sides opposite the angles are given lower case letters. B a c C b A

  5. The Theorem of Pythagoras Capital letters are used for angles. The sides opposite the angles are given lower case letters. B a c C b A

  6. The Theorem of Pythagoras Draw to scale the right angled triangle shown below. Measure the length of side ‘a’. What do you get? a cm 3 cm 5 cm. 4 cm Measure the length of side ‘b’. What do you get? b cm 9 cm 15 cm 12 cm

  7. Born: about 569 BC in Samos, IoniaDied: about 475 BC It was Pythagoras who discovered the link between the lengths of the sides in a right angled triangle. Because of this the formula carries his name. The formula is known as the ‘Theorem of Pythagoras’.

  8. a c b Always START with the hypotenuse

  9. r t s

  10. v x w

  11. b a c

  12. In a right angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

  13. 1. Calculate the lengths of the hypotenuse in the following triangles. 5 cm 7 cm (ii) (i) (iii) 7 cm 4 cm 8 cm 3 cm

  14. 2. Calculate the lengths of the marked side in the following triangles. (ii) (i) 13 cm 9 cm 15 cm 5 cm

  15. Page 71 Exercise 2A

  16. 3. Calculate x in the diagram below. There are no right angled triangles. 13 cm We need to make one. 10 cm 13 cm 5 cm

  17. Page 72 Exercise 2B

  18. Calculating distance using coordinates How do we calculate the length of the line? Let’s make a right angled triangle. Now we can measure the horizontal and vertical distance. We can now use the theorem of Pythagoras to calculate the distance between the two points. 4 3

  19. Page 75 Exercise 4A

  20. The Converse of the Theorem of Pythagoras The theorem In a right angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. The converse If in a triangle, the square of the largest side is equal to the sum of the squares of the other two sides, then the triangle is right angled.

  21. 1. Use the converse of Pythagoras to show that the triangle below is right angled. B 15 cm 9 cm C 12 cm A Longest side: Shorter sides: Hence the triangle is right angled by the converse of Pythagoras.

  22. Page 79 Exercise 5A

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