The sum of the lengths of any two sides is greater than the lenght of the third side.

For all triangles,

by cosine rule,

c²=a²+b²-2abcosC

(a+b)²=a²+2ab+b²

a+b=√(a²+2ab+b²)

c=√(a²+b²-2abcosC)

now, a+b is definitely larger than c, as the maximum possible value of -2abcosC is less than 2ab, as angle C is smaller than 180 but larger than 0.