Question 493573
To prove that the hypotenuse is the longest side of a right triangle, we use the Pythagorean theorem


*[tex \LARGE c^2 = a^2 + b^2]


and the fact that *[tex \LARGE c^2 > a^2] implies *[tex \LARGE a^2 + b^2 > a^2 \Rightarrow b^2 > 0] (sometimes called the "trivial" inequality).


If you are not allowed to use the Pythagorean theorem, use the law of cosines and claim that the Pythagorean theorem is a special case of the law of cosines.