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 8, 1, 7 8, 1, 7 2, 7, 6 2, 7, 6 12, 10, 22
The Triangle Inequality 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.
Let's apply the Triangle Inequality Theorem to each group of side measures:
1) 9, 4, 3: 9 + 4 = 13 > 3, 9 + 3 = 12 > 4, 4 + 3 = 7 < 9
- This group of side measures forms a triangle.
2) 8, 1, 7: 8 + 1 = 9 > 7, 8 + 7 = 15 > 1, 1 + 7 = 8 > 1
- This group of side measures forms a triangle.
3) 2, 7, 6: 2 + 7 = 9 > 6, 2 + 6 = 8 > 7, 7 + 6 = 13 > 2
- This group of side measures forms a triangle.
4) 12, 10, 22: 12 + 10 = 22 > 22, 12 + 22 = 34 > 10, 10 + 22 = 32 > 12
- This group of side measures does NOT form a triangle.
answer the question
The groups of side measures that will form a triangle based on the Triangle Inequality Theorem are:
1) 9, 4, 3
2) 8, 1, 7
3) 2, 7, 6