Question

How to prove pythagoras theorem?

Answer 1

If we take a right angled triangle.

The Pythagorean Theorem states that, in a right triangle, the square of a $\left(a^2\right)$ plus the square of b $\left(b^2\right)$ is equal to the square of c
$\left(c^2\right):$
$a^2+b^2=c^2$
Four such right angled triangle can be arranged as

Area of Whole Square
It is a big square, with each side having a length of a+b, so the total area is:
A = (a+b)(a+b)
Area of The Pieces
Now let's add up the areas of all the smaller pieces:
Area of small square =$c^2$
Area of four triangles = $4\times (\frac{1}{2}\times a\times b)$
So $c^2+2ab=(a+b{)}^2$
$\Rightarrow a^2+b^2=c^2$