Three line segments, of lengths a, b, and c, can form a triangle as long as no one length is greater than the sum of the other two (the shortest distance between two points is a straight line). But if it is certainly true that the longest side is c and c< a+ b. A right triangle is a triangle as Plato said.
(To see that leads to [as long as neither of a or b is 0], add the positive number 2ab to both sides of . You get . Since is larger than , a+ b is larger than c.)