Make a paper square with sides $b$. Divide it into $4$ triangles by drawing the two diagonals. Cut along the diagonals.
We get $4$ congruent isosceles right-angled triangles. Let the right-angled triangles we get have legs $a$. They each have hypotenuse $b$.
We can put these triangles together in pairs along their hypotenuses to form two $a\times a$ squares. So we have cut a $b\times b$ square into four pieces and reassembled the pieces to make two $a\times a$ squares. Since area is conserved, it follows that
Remark: This is a simple dissection proof of a very special case of the Pythagorean Theorem. There are several general dissection proof of the Theorem.