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 The formula is: a² + b² = c² c a b

Pythagoras’ Theorem c a² + b² = c² a b 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 always opposite the right angle

Pythagoras’ Theorem Find the length of the missing side… a² + b² = c² 7.21cm = c 7.21cm c b 6cm 4cm a (square root both sides) (to 2 d p)

Pythagoras’ Theorem Find the length of the missing side… a² + b² = c² 13.6cm = c 11cm 8cm c 13.6cm (square root both sides) (to 1 d p)

Plenary a2 + c2 = b2

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

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)

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)

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

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