pythagoras' theorem © victoria smith begin. right angled triangles pythagoras’ theorum will...

Pythagoras' Theorem

© V

ictor

ia S

mith

Begin

Right Angled TrianglesPythagoras’ Theorum will only work on a right angled triangle.

a c

bThe longest side, opposite the right angle is the hypotenuse.

Formula

© V

ictor

ia S

mith

Formula

a c

b a2 + b2 = c2

Alternatively a2 = c2 - b2 or b2 = c2 - a2

Examples

© V

ictor

ia S

mith

Easy Examples

x3

4

x2 = 32 + 42

Next

© V

ictor

ia S

mith

Easy Examples

x3

4

x2 = 32 + 42 x2 = 9 + 16

Next

© V

ictor

ia S

mith

Easy Examples

x3

4

x2 = 32 + 42 x2 = 9 + 16x2 = 25

Next

© V

ictor

ia S

mith

Easy Examples

x3

4

x2 = 32 + 42 x2 = 9 + 16x2 = 25x = 5

Next

© V

ictor

ia S

mith

Easy Examples

x3

4

x2 = 32 + 42 x2 = 9 + 16x2 = 25x =5

x

68

x2 = 62 + 82

Next

© V

ictor

ia S

mith

Easy Examples

x3

4

x2 = 32 + 42 x2 = 9 + 16x2 = 25x = 5

x

68

x2 = 62 + 82 x2 = 36 + 64

Next

© V

ictor

ia S

mith

Easy Examples

x3

4

x2 = 32 + 42 x2 = 9 + 16x2 = 25x = 5

x6

8

x2 = 62 + 82 x2 = 36 + 64x2 = 100

Next

© V

ictor

ia S

mith

Easy Examples

x3

4

x2 = 32 + 42 x2 = 9 + 16x2 = 25x = 5

x6

8

x2 = 62 + 82 x2 = 36 + 64x2 = 100x = 10

Harder

© V

ictor

ia S

mith

Harder Example

x7

24

x2 = 72 + 242

Next

© V

ictor

ia S

mith

Harder Example

x7

24

x2 = 72 + 242 x2 = 49 + 576

Next

© V

ictor

ia S

mith

Harder Example

x7

24

x2 = 72 + 242 x2 = 49 + 576x2 = 625

Next

© V

ictor

ia S

mith

Harder Example

x7

24

x2 = 72 + 242 x2 = 49 + 576x2 = 625x = 25

Next

© V

ictor

ia S

mith

Harder Example

x7

24

x2 = 72 + 242 x2 = 49 + 576x2 = 625x = 25

What happens if x is not the hypotenuse?

Continue

© V

ictor

ia S

mith

Rearranging the FormulaIf x is not assigned the hypotenuse, you will need to rearrange the formula:

1118

x

112 = 182 + x2

Next

© V

ictor

ia S

mith

Rearranging the FormulaIf x is not assigned the hypotenuse, you will need to rearrange the formula:

1118

x

112 = 182 + x2 x2 = 182 - 112

Next

© V

ictor

ia S

mith

Rearranging the FormulaIf x is not assigned the hypotenuse, you will need to rearrange the formula:

1118

x

112 = 182 + x2 x2 = 182 - 112 x2 = 324 - 121

Next

© V

ictor

ia S

mith

Rearranging the FormulaIf x is not assigned the hypotenuse, you will need to rearrange the formula:

1118

x

112 = 182 + x2 x2 = 182 - 112 x2 = 324 - 121x2 = 203

Next

© V

ictor

ia S

mith

Rearranging the FormulaIf x is not assigned the hypotenuse, you will need to rearrange the formula:

1118

x

112 = 182 + x2 x2 = 182 - 112 x2 = 324 - 121x2 = 203x= 14.24

Summary

© V

ictor

ia S

mith

Summary

• Only works on right angled triangles• The formula is a2 + b2 = c2

• If the side you are looking for is not the hypotenuse, you must rearrange the formula

© V

ictor

ia S

mith