A. determine if the combined length of any two sides is greater than the length of the third side
To find the validity of a triangle with sides of lengths denoted as ∆ABC, one of the initial steps is to apply the triangle inequality theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. In other words:
For a triangle with sides of lengths a, b, and c:
a + b > c
a + c > b
b + c > a
If this condition is not met for any of the three pairs of sides, then the triangle with the given side lengths is not possible or valid.
Option A correctly suggests determining if the combined length of any two sides is greater than the length of the third side, which is a crucial step in determining the validity of a triangle. This is the most appropriate option for finding the incidence of ∆ABC among the given choices.