### Theory:

In sixth century B.C., a Greek philosopher Pythagoras had done a amazing discovery over right triangle.
In a right-angled triangle, the sum of the square on the legs is equal to the square on the hypotenuse.

Let's us experiment the Pythagoras theorem.

Draw a right angled triangle $$ABC$$.

Here $$AB = a, BC = b$$ and $$AC = c$$.

The legs are $$AB$$ and $$BC$$. The hypotenuse is $$AC$$.

Let's find the square of each side and verify the provided theorem.

As $$AB = a$$, $$BC = b$$ and $$AC = c$$, the square of each side becomes $$a²$$, $$b²$$ and $$c²$$.

If we draw this case in graph paper, it would give the result as area of the square with side length $$AC$$ is equal to the sum of area of the square with side length $$AB$$ and the area of square with side length $$BC$$.

That is, square on the hypotenuse ($$c²$$) is equal to the sum of square on the legs ($$a²+b²$$).

Thus, $$a²+b²=c²$$.
Important!
The converse of the Pythagoras theorem hold. This implies, 'if the Pythagoras property holds, the triangle must be right-angled triangle'.