Final Answer:
Compare the sum of the smallest and middle numbers to the largest number (Option a).
Step-by-step explanation:
To determine if a set of three numbers can form a triangle, you would begin by applying the Triangle Inequality Theorem. This theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. Option A, comparing the sum of the smallest and middle numbers to the largest number, aligns with this principle. If the sum of the two smaller numbers is greater than the largest number, it satisfies the condition for a valid triangle (Option a).
For example, let the three numbers be represented as a₁, b₁, and c₁, where a₁ ≤ b₁ ≤ c₁. To check the Triangle Inequality, you would compare a₁ + b₁ to c₁. If a₁ + b₁ > c₁, then the set of numbers can form a triangle. This approach ensures that the sum of the two shorter sides is greater than the longest side, a fundamental requirement for a geometric figure to be a triangle.
In conclusion, option A provides a reliable and straightforward method for assessing whether a set of three numbers can form a triangle, making it a suitable choice for the initial step in solving this geometric problem.