Question

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

Answer 1

To determine which groups of side measures can form a triangle, we will apply the Triangle Inequality Theorem. This theorem states that for any triangle with sides \( a \), \( b \), and \( c \), the following must be true:

1. \( a + b > c \)
2. \( a + c > b \)
3. \( b + c > a \)

Let's analyze each group of side measures given:

1. **8, 1, 7**:
- \( 8 + 1 = 9 > 7 \) (True)
- \( 8 + 7 = 15 > 1 \) (True)
- \( 1 + 7 = 8 \not> 8 \) (False)
- **Cannot form a triangle.**

2. **12, 10, 22**:
- \( 12 + 10 = 22 \not> 22 \) (False)
- **Cannot form a triangle.**

3. **2, 7, 6**:
- \( 2 + 7 = 9 > 6 \) (True)
- \( 2 + 6 = 8 > 7 \) (True)
- \( 6 + 7 = 13 > 2 \) (True)
- **Can form a triangle.**

4. **9, 4, 3**:
- \( 9 + 4 = 13 > 3 \) (True)
- \( 9 + 3 = 12 > 4 \) (True)
- \( 4 + 3 = 7 < 9 \) (False)
- **Cannot form a triangle.**

Only the side measures **2, 7, 6** can form a triangle.