If a triangle has side lengths a b and c and if a2 plus b2 equals c2 then the says that the triangle is a right triangle?

no because even if a2 and b2 both add up to c2, it doesnt mean that they are the same length. one could be long and the other short but still add up to c2. a2 and c2 have to be equal to be a right angle.

(apex) converse to the Pythagorean theorem