Geometry

Question Analysis

The principal aim is to utilize the Triangle Inequality Theorem to identify which set of side lengths can construct a triangle. This necessitates verifying if the sum of any two sides within each set surpasses the third side.

Key Concept Explanation

The Triangle Inequality Theorem stipulates that for any triangle with side lengths , , and , the three inequalities a + b>c, a + c>b, and b + c>a must all be satisfied. Geometrically, this theorem ensures that the sides can connect to form a closed - loop shape.

Step - by - Step Solution

1. For the set :

Calculate . Since  is not greater than , it fails to meet the requirements of the the...