The blue, purple, green, and pink triangles are all equal triangles. The triangles on the left combine to form a square with length c (the hypotenuse) on each side. Therefore, the area of square (c^2) is given in the middle. The triangles on the right are the same triangles as on the left, just simply rearranged to show two smaller squares, one with sides of length a and the other with sides of length b. Therefore, the squares on the right are of areas equal to a^2 and b^2, respectively. The Pythagorean Theorem is proved by noting that the area of c^2 is equal to the sum of the areas a^2 and b^2. Credit for demonstration of this theorem and how to manipulate objects in GeoGebra goes to Doug Stevens (https://www.youtube.com/watch?v=I34-TRgBuN8&noredirect=1).
