Question

Apply the Triangle Inequality Theorem and determine which group of side measures will form a triangle.
Responses
9, 4, 3
2, 7, 6
8, 1, 7
12, 10, 22

Answer 1

really? 4 + 3 = 7 > 9 ??
1 + 7 = 8 < 8 ???
12 + 10 = 22 > 22 ???
None of these can form a triangle.
Only B works, since 6-2 < 7 < 6+2

Answer 2

Based on the Triangle Inequality Theorem, 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 this theorem to the given groups of side measures:

1. For side measures 9, 4, 3:
9 + 4 = 13 > 3
9 + 3 = 12 > 4
4 + 3 = 7 > 9

Therefore, 9, 4, 3 can form a triangle.

2. For side measures 2, 7, 6:
2 + 7 = 9 > 6
2 + 6 = 8 < 7
7 + 6 = 13 > 2

Therefore, 2, 7, 6 can form a triangle.

3. For side measures 8, 1, 7:
8 + 1 = 9 > 7
8 + 7 = 15 > 1
1 + 7 = 8 < 8

Therefore, 8, 1, 7 can form a triangle.

4. For side measures 12, 10, 22:
12 + 10 = 22 > 22
12 + 22 = 34 > 10
10 + 22 = 32 > 12

Therefore, 12, 10, 22 can form a triangle.

In conclusion, all four groups of side measures can form triangles according to the Triangle Inequality Theorem.

Answer 3

Apologies for the errors in my initial response. Thank you for correcting them.

To clarify:
- 9, 4, 3 cannot form a triangle because 4 + 3 is not greater than 9.
- 8, 1, 7 cannot form a triangle because 1 + 7 is not greater than 8.
- 12, 10, 22 cannot form a triangle because 12 + 10 is not greater than 22.

The only group of side measures that can form a triangle according to the Triangle Inequality Theorem is 2, 7, 6 since 6 - 2 is less than 7 and 7 is less than 6 + 2.