Pythagoras' states: . If we want to obtain the hypotenuse, c, we need to take squares on both sides. It's just inherent in the definition of the hypotenuse:
Good day! Im a noob in math so i just want to ask this simple question. I know that Pythagorean theorem is the sum of the areas of 2 squares on the legs equals to the area of the square on the hypotenuse. My question is; why did they refer to a square to prove the a theorem that is being used into a triangle? thanks in advance.
You can find several proofs of the theorem here:
Pythagorean theorem - Wikipedia, the free encyclopedia
(My personal favorite is the one titled "Algebraic Proof".)
We don't have to use this method of proof, as awkward has pointed out, there are many proofs of the theorem. It just so happens that the proof you mention is a popular and simple one. If you still want to worry about it, think about how a right-angled triangle relates to a rectangle/square. Could a square be built out of triangles, and vice-versa?