Consider the right triangle ABC.
On the short side AB add a right-angled triangle ABD similar to ACB.
As 
is similar to 
,
. Rearranging
this equation gives:
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Angle DBC = 90º. Thus triangle DBC is similar to 
and 
. Rearranging
this equation gives .
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Recall that the area of a triangle equals one half the base times the height.
So area()
+ area() =
area(
), gives
Replacing AD and BD with their values in the equations above we obtain:
Dividing both sides by 
then leads to
Pythagoras Theorem