The contents of the package. ASU copyright

The squares of the two sides added together. ASU copyright

The area is completely filled with four yellow triangles and a blue box. The hypotneuse of the yellow triangles and the side of the box is c. ASU copyright

The yellow triangles are rearanged. The area not covered by the yellow triangles is equal to the blue square with side c and area c^2. The small box is the square of the short leg of the triangle a and area a^2. The other box is the square of b. ASU copyright

The blue square has area (b-a)^2. The red triangles have area 2(ab)^2. The box that holds the blue box and 4 triangles is c^2. A little algebra with show c^2=a^2+b^2. ASU copyright