pythagoras' theorem © victoria smith begin. right angled triangles pythagoras’ theorum will...
DESCRIPTION
Formula ac b a 2 + b 2 = c 2 Alternatively a 2 = c 2 - b 2 orb 2 = c 2 - a 2 Examples © Victoria SmithTRANSCRIPT
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
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ictor
ia S
mith
Easy Examples
x3
4
x2 = 32 + 42
Next
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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
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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