This proof process should use the thinking mode of area method:

There are three squares in the picture, one is the big square outside, and the side length is (a+b); There are two small squares in the middle, one with a side length of B and the other with a side length of C, and there are four small right triangles in the picture.

According to the area method, the area of a square with a middle side length of c is equal to the area of a big square minus the areas of four small triangles on its sides.

The area of a square with side length c is c 2,

The area of a big square is (a+b) 2, the areas of four small triangles are 4*0.5*a*b, and the subtraction of the two formulas is A 2+B 2;

Therefore, C 2 = A 2+B 2 (get)