PYTHAGORAS.

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Presentation transcript:

PYTHAGORAS

Pythagoras’ theorem is used when you know two sides in a right-angled triangle and you want to find the length of the third side. The longest side in a right-angled triangle is called the hypotenuse. c a b Pythagoras discovered that….

The sum of the areas of the squares on the two shorter sides is equal to the area of the square on the hypotenuse. c a b

Example 1 Calculate the value of x. x 2 cm 6 cm

Example 2 Calculate the value of x. x 10 cm 5 cm

Example 3 Calculate the value of x. x 4 cm 9 cm

Example 4 Calculate the value of x. x 3.2 cm 7.6 cm

Example 5 Calculate the value of x. x x 8 cm

Example 6 The equilateral triangle has sides of length 6 cm. Calculate a the height of the triangle b the area of the triangle. 6 cm h a 3 cm b

7 Find the length of the line joining (−4, 4) and (3, 1). Example 7 Find the length of the line joining (−4, 4) and (3, 1). 2 -2 -4 4 x 3 7

To find the length of AG you need to look at triangle AGC. Pythagoras in 3-D To find the length of AG you need to look at triangle AGC. A B C E G H D F 7 cm 6 cm 5 cm A B C E G H D F 7 cm 6 cm 5 cm First you need to calculate AC using Pythagoras on triangle ABC. Now use Pythagoras on triangle ACG. A C G 5 cm

It is useful to remember that AG can be calculated directly using: 7 cm 6 cm 5 cm It is useful to remember that AG can be calculated directly using: