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Square Numbers To SQUARE a number means to multiply it by itself For example the square of 7 is 7 7 = 49 We shorten this to 7 2 = 7 7 = 49 We read 7 2 as seven squared.

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Because a square has equal sides we can use : l l

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Calculate the area of the shape below. 4cm 8cm

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Page 151 Exercise 1

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Square Roots ( ) We know how to find 7 2 = 49, but what if we want to know which number times itself gives 49? We can see from above that the answer is 7 We say “the square root of 49 is 7” We shorten this to

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Sometimes we have to use a calculator to find the square root. Page 153 Exercise 2

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Pythagoras Theorem Pythagoras was a famous Greek mathematician who discovered an amazing connection between the three sides of a right angled triangle. This connection means it is possible to CALCULATE the length of one side of a right angled triangle as long as you know the lengths of the other two.

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The longest side is opposite the largest angle This side is known as the HYPOTENUSE Let us look at the lengths of the sides. 3cm 4cm 5cm We can see that CHECK

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Page 154 Exercise 3

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a cm b cm c cm We can use this rule to calculate the length of the hypotenuse if we know the length of the other two sides.

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Calculate the length of the hypotenuse in the triangle. 8cm 6cm c

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Remember: Always label the sides and note which one is the hypotenuse. Starting with the hypotenuse, write out the Theorem of Pythagoras. Use this formula to calculate the length of the side. b a c a b c

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Page 156 Exercise 4

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Problems involving Pythagoras 2 m 1.5 m A ladder is resting against a wall. Calculate the length of the ladder. 1.5 m 2 m a

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A helicopter leaves Aberdeen. It flies East for 30 km then North for 40km. How far is the helicopter from Aberdeen? 30km 40km d Aberdeen Page 159 Exercise 5

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Finding the Length of Other Sides c b 13 cm and x 12 cm a

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15 cm y cm 9 cm Page 161 Exercise 6

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Pythagoras Theorem Reminder of square numbers: 1 2 = 1 x 1 = 1 2 2 = 2 x 2 = 4 3 2 = 3 x 3 = 9 4 2 = 4 x 4 = 16 3232 Base number Index number The index.

Pythagoras Theorem Reminder of square numbers: 1 2 = 1 x 1 = 1 2 2 = 2 x 2 = 4 3 2 = 3 x 3 = 9 4 2 = 4 x 4 = 16 3232 Base number Index number The index.

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