Proof of Pythagoras Theorem
![](/o-level-maths/proof-of-pythagoras-theorem-html-15b84e84.gif)
The large squares above both have equal areas since both are of side
To produce the large square on the right arrange the red and blue triangles from the square above left around the outside as shown.The area of the large square above left is given by
The area of the large square above right is given by
or
Equating these two gives
Expanding and simplifying gives
and cancelling
from both sides gives
- this is Pythagoras theoremNote that
are the sides of one of the red or blue right angled triangles, with
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