Explain Pythagorean Theorem Proof Practice Test

In a right triangle, the legs are labeled $a$ and $b$ and the hypotenuse is labeled $c$. A student writes the proof step: “The area of the large square is $a^2+b^2$.” What is the best correction for an area-based proof using a large square of side $(a+b)$?

A student claims that the following argument proves the Pythagorean theorem: 'In any right triangle, the square of the hypotenuse equals the sum of the squares of the other two sides because this relationship defines what makes a triangle a right triangle.' What is the primary flaw in this reasoning?