Bhaskara’s 1^st Proof

He used the following diagrams in proving the Pythagorean Theorem.

In the above diagrams, the blue triangles are all congruent and the yellow squares are congruent.

First we need to find the area of the big square two different ways.

First let's find the area using the area formula for a square.

Area=c^2.

Now, lets find the area by finding the area of each of the components and then sum the areas.

Area of the blue triangles = 4(1/2)ab

Area of the yellow square = (b-a)^2

Therefore,

Area of the big square = 4(1/2)ab + (b-a)^2

= 2ab + b^2 - 2ab + a^2

= b^2 + a^2

Since, the square has the same area no matter how you find it

Area = c^2 = a^2 + b^2