Question
Can the Triangle Inequality Theorem be used to determine if a set of side lengths can form a triangle?
Answers
GPT-4o mini
Yes, the Triangle Inequality Theorem can indeed be used to determine if a set of side lengths can form a triangle. The theorem states that for any three lengths \(a\), \(b\), and \(c\) to form a triangle, the following conditions must be satisfied:
1. \(a + b > c\)
2. \(a + c > b\)
3. \(b + c > a\)
If all three conditions are met, then the side lengths can indeed form a triangle. If any one of these inequalities is not satisfied, then the lengths cannot form a triangle.
1. \(a + b > c\)
2. \(a + c > b\)
3. \(b + c > a\)
If all three conditions are met, then the side lengths can indeed form a triangle. If any one of these inequalities is not satisfied, then the lengths cannot form a triangle.