Answer:
Remember that the Pythagorean's theorem says that:
For a triangle rectangle with hypotenuse H and catheti A and B:
H^2 = A^2 + B^2
Here we also need to remember that the area of a square of side length L is:
area = L^2
Now let's solve this.
First, we start with two squares, one of side length a and the other of side length b.
Such that the complete area in the first image is:
area = a^2 + b^2
Now we draw two triangle rectangles with catheti a and b, and with hypotenuse c.
in step 3, we rotate those triangles in order to make a larger square, with side length c, with an area equal to:
area = c^2
Notice that we never added more shapes, so the area of the image did not change in all this process, then the initial area must be equal to the final area:
a^2 + b^2 = area = c^2
a^2 + b^2 = c^2
And remember that a and b are the catheti of the triangles, and c is the hypotenuse, then this is the Pythagorean's theorem.
