1. PYTHAGORAS

2. 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….

3. 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

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

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

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

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

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

9. 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

10. 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

11. 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

12. 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: