The Theorem Of Pythagoras The Theorem Of Pythagoras

  • Slides: 10
Download presentation
The Theorem Of Pythagoras.

The Theorem Of Pythagoras.

The Theorem Of Pythagoras. w Pythagoras was a Greek Mathematician. (580 -500 B. C).

The Theorem Of Pythagoras. w Pythagoras was a Greek Mathematician. (580 -500 B. C). 2500 years old is even older than your teacher. w He was eccentric. (mad!!) Don’t mention √ 2 to him!! w He discovered an amazing rule about right angled triangles. w By completing the table opposite you are going to make the discovery for yourself. c b a a b 3 4 5 12 6 10 8 15 c a 2 b 2 c 2

Complete the results of your table below: a b c a 2 b 2

Complete the results of your table below: a b c a 2 b 2 c 2 3 4 5 9 16 25 5 12 13 25 144 169 6 8 10 36 64 100 8 15 17 64 225 289 By considering all the numbers in the completed table can you see what Pythagoras discovered ? Theorem Of Pythagoras: a 2 + b 2 = c 2

Calculating An Unknown Side. w The longest side of a right angled triangle is

Calculating An Unknown Side. w The longest side of a right angled triangle is called the hypotenuse. w. Pythagoras discovered that the sum of the squares of the two shorter sides is equal to the square of the hypotenuse. HYPOTENUSE c a b a 2 + b 2 = c 2

A 6 Find the side A in this triangle. 8 Solution. A 2 =

A 6 Find the side A in this triangle. 8 Solution. A 2 = 8 2 + 6 2 A 2 = 64 + 36 A 2= 100 A = √ 100 A =10 Hint Follow this routine exactly every time to solve Pythagoras problems easily.

What Goes In The Box? Find the length of side W in this right

What Goes In The Box? Find the length of side W in this right angled triangle. W 2 = 6. 42 + 5. 82 W 2 = 40. 96 + 33. 64 W 2 = 74. 6 W = 8. 6 cm W 6. 4 cm 5. 8 cm

Find the unknown side in each of the triangles below. (1) (2) 12. 04

Find the unknown side in each of the triangles below. (1) (2) 12. 04 A 9. 22 8 B (3) 9 7 10. 73 C 24. 7 (5) 6 E 8. 9 22. 7 23 6. 8 (4) 9 24. 38 D 8. 3

Finding A Shorter Side. Calculate the length of side W. W 2 + 12.

Finding A Shorter Side. Calculate the length of side W. W 2 + 12. 32 = 14. 7 2 14. 7 m W 2 + 151. 29 = 216. 09 W 2 = 216. 09 – 151. 29 W W= √ 64. 8 W = 8. 05 m 12. 3 m

What Goes In The Box? 2 Find the length of side H in the

What Goes In The Box? 2 Find the length of side H in the right angled triangle below: 3. 4 m 2. 6 m H H 2 + 2. 62 = 3. 42 H 2 + 6. 76 = 11. 56 H 2 = 11. 56 - 6. 76 H 2 = 4. 8 H = 2. 19 m

Calculate the size of the shorter side in the following. (1) 13. 59 m

Calculate the size of the shorter side in the following. (1) 13. 59 m 9. 2 cm 14. 4 m (2) 12. 4 cm (3) A 9 mm C 8. 3 cm D 19. 8 m 11. 2 mm (5) 27. 6 m (4) B 6. 7 mm E 35. 7 m 22. 6 m 11. 9 cm 8. 6 cm 14. 7 cm