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3 B’s B4 Me

Pythagoras’ Theorem. 22/11/2012. Find : (to 1.d.p) 3² = b) 7² = c) 3.45² = d) 9² = e) 10² = f) 20² = g) 2.1 ² = Find: √ 9 = b) √7 = c) √36= d) √2 = e) √1.456 = f) √2.5 g) √64 =.

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3 B’s B4 Me

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  1. Pythagoras’ Theorem 22/11/2012 Find: (to 1.d.p) 3² = b) 7² = c) 3.45² = d) 9² = e) 10² = f) 20² = g) 2.1 ² = Find: √9 = b) √7 = c) √36= d) √2= e) √1.456 = f) √2.5 g) √64 = 3 B’s B4 Me

  2. Pythagoras’ Theorem 22/11/2012 Find: 9 b) 49 c) 11.9 d) 81 e) 100 f) 400 g) 4.4 Find: 3 b) 2.6 c) 6d) 1.4 e) 1.2 f) 1.6 g) 8 3 B’s B4 Me

  3. Criteria for Success • To know what Pythagoras theorem is and use it to find the length of the hypotenuse • To know how to use Pythagoras theorem to show whether a triangle is right-angled. • To find out what Pythagoras proved using powers of investigation!

  4. Keywords Pythagoras Hypotenuse Square Right Angle Square Root Investigate Theorem Prove 3 B’s B4 Me

  5. Pythagoras’ Theorem I was born at Samos, in Greece, and lived from 580 to 500 B.C. I was a Mathematician who became famous for discovering something unique about right – angled triangles. Now you are going to try to find out what I discovered!! 3 B’s B4 Me

  6. The Hypotenuse The longest side opposite the right angle is called the hypotenuse. b a z c x b a y c 3 B’s B4 Me

  7. Make accurate copies of the three right-angled triangles below 3 1 2 6cm Can you see a pattern in the last 3 columns? If you can then you have rediscovered Pythagoras’ Theorem 5cm Next measure the length of the longest side of each one. Then complete the table under activity one on your sheet! 3cm a 4cm b 12cm 8cm c 4

  8. Using Pythagoras’ Theorem c a Area C c2 a2 + b2 = c2 So what is Pythagoras’ Theorem? He said that: “For any right triangle, the sum of the areas of the two small squares is equal to the area of the larger.” Pythagoras b Area A a2 Area B b2

  9. Using Pythagoras’ Theorem Area C 9 +16 = 25 Find the Length of side x We can use Pythagoras’ Theorem to find the longest side in a right –angled triangle How do we get the length of side x x =25 = 5cm Area A 32 = 9 x 3cm 4cm Area B 42 = 16

  10. Using Pythagoras’ Theorem Example We can use Pythagoras’ Theorem to find the longest side in a right –angled triangle x Find the Length of side x 7cm 9cm

  11. Applying your knowledge 1. Complete activity two on your worksheet 2. Complete the questions below 3. Begin activity three! See how far you can get!

  12. All about the right-angle… A. B. 3cm 5cm 8cm 7.5cm 5.8cm One of these is a right-angle, how do we show which one? 4.5cm Now complete activity 3 on the sheet.

  13. And to finish… x cm How can we find out the shorter side? 8cm 10cm

  14. Lesson Outcomes • I am able to apply my knowledge of maths to different situations. • I can calculate a missing hypotenuse on a right-angled triangle • I am able to use Pythagoras to identify whether a triangle has a right angle. 3 B’s B4 Me

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