The Triangle Inequality Theorem states that the sum of any 2 sides of a triangle must be greater than the measure of the third side. Let's say side a = 1.2, b = 1.9, and c = 3.1, if we add a+b, then the sums are equal to side c. This would not satisfy the Triangle Inequality Theorem because one configuration of the equation results in the sum and third length being congruent, rather than greater.
