#1**0 **

Make a diagram like this:

The area of the entire square is \((a+b)^2 = a^2 + b^2 + 2ab\)

The area can also be represented as the sum of the area of the 4 triangles and the square in the middle: \(c^2 + 2ab\)

Since they both represent the area of the square, we have the equation \(a^2 + b^2 + 2ab = c^2 + 2ab\)

Subtracting 2ab from both sides gives us \(\color{brown}\boxed{a^2 + b^2 = c^2}\)

BuilderBoi Aug 29, 2022