Apply the Triangle Inequality Theorem and determine which group of side measures will form a triangle.(1 point) Responses 9, 4, 3 9, 4, 3 2, 7, 6 2, 7, 6 12, 10, 22 12, 10, 22 8, 1, 7 8, 1, 7
According to the Triangle Inequality Theorem, for a triangle to be formed, the sum of the lengths of any two sides must be greater than the length of the third side.
Applying the theorem to the given sets of side measures:
1. 9, 4, 3: This set does form a triangle because 9+4 > 3, 9+3 > 4, and 4+3 > 9. So, it satisfies the inequality.
2. 2, 7, 6: This set forms a triangle because 2+7 > 6, 2+6 > 7, and 7+6 > 2.
3. 12, 10, 22: This set forms a triangle because 12+10 > 22, 12+22 > 10, and 10+22 > 12.
4. 8, 1, 7: This set forms a triangle because 8+1 > 7, 8+7 > 1, and 1+7 > 8.
Conclusion: All of the given groups of side measures (9, 4, 3), (2, 7, 6), (12, 10, 22), and (8, 1, 7) will form a triangle.