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Pythagoras' Theorem

Pythagoras' Theorem. Starter. In your book, Draw a Horizontal Line measuring 4cm Then, on one end of the line, draw a 3cm Vertical line What is the distance between the two unjoined ends?. Pythagoras’ Theorem. Pythagoras’ Theorem links the lengths of 3 sides of a Right Angled Triangle

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Pythagoras' Theorem

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  1. Pythagoras' Theorem

  2. Starter • In your book, Draw a Horizontal Line measuring 4cm • Then, on one end of the line, draw a 3cm Vertical line • What is the distance between the two unjoined ends?

  3. Pythagoras’ Theorem • Pythagoras’ Theorem links the lengths of 3 sides of a Right Angled Triangle • The formula is: a² + b² = c² c a b

  4. Pythagoras’ Theorem • It does not matter which way round we put a and b, as long as side c is the longest side • We call side c the HYPOTENUSE • It is alwaysopposite the right angle c a² + b² = c² a b

  5. Pythagoras’ Theorem • Find the length of the missing side… a² + b² = c² 4² + 6² = c² 16 + 36 = c² 52 = c² 7.211102 = c 7.21cm = c 7.21cm c b 6cm 4cm a (square root both sides) (to 2 d p)

  6. Pythagoras’ Theorem b a • Find the length of the missing side… a² + b² = c² 8² + 11² = c² 64 + 121 = c² 185 = c² 13.60147 = c 13.6cm = c 11cm 8cm c 13.6cm (square root both sides) (to 1 d p)

  7. Plenary a2 + c2 = b2

  8. Plenary Because 75º + 25º = 100º, so the missing Angle is 80º. Pythagoras’ Theorem only works in Right-Angled Triangles

  9. Pythagoras’ Theorem • Finding a shorter side… c • Find the length of the missing side… • c² - b² = a² • 8² - 6² = a² • 64 - 36 = a² • 28 = a² • 5.291502… = a • 5.29cm = a 8cm b 6cm 5.29cm a (square root both sides) (to 2 d p)

  10. Pythagoras’ Theorem • Finding a shorter side… b a 10.82cm 2cm • Find the length of the missing side… • c² - a² = b² • 11² - 2² = b² • 121 - 4 = b² • 117 = b² • 10.81665383 = b • 10.82cm = b 11cm c (square root both sides) (to 2 d p)

  11. Plenary • In your books, sketch a set of axes and plot on them the coordinates (2,1) and (5,8) • Calculate the distance between the 2 coordinates (5,8) (2,1) a2 + b2 = c2 7 32 + 72 = c2 58 = c2 3 7.62 = c

  12. Summary • We have learnt how to use Pythagoras’ Theorem to find missing sides in right-angled triangles • Next lesson we will look at some worded questions

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