Below is a walkthrough of how the Chinese were able to prove the Pythagorean relationship. The proof is similar to that of the Pythagoreans, however, it is to be noted that these proofs were developed in isolation from each other. That is, that the Greeks and Chinese likely did not influence each other in their understanding and discovery of this relationship.

What is the area of the square formed on side a of the triangle (the red square)? What is the area of the square formed on side b of the triangle (the green square)?
What What is the sum of these two values?
What is the value of the square formed by side c, the hypotenuse (the blue square)?