Question

Identify the side measures that will not form a triangle.(1 point)
Responses

4, 4, 5
4, 4, 5

4, 4, 6
4, 4, 6

4, 4, 7
4, 4, 7

4, 4, 8

Answer 1

To determine which set of side measures cannot form a triangle, we can apply the triangle inequality theorem. This theorem states that for any three sides \(a\), \(b\), and \(c\) of a triangle, the following conditions must be met:

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

Let's evaluate each set of side measures.

1. **4, 4, 5**
- \(4 + 4 > 5\) (True)
- \(4 + 5 > 4\) (True)
- \(4 + 5 > 4\) (True)
- This set can form a triangle.

2. **4, 4, 6**
- \(4 + 4 > 6\) (True)
- \(4 + 6 > 4\) (True)
- \(4 + 6 > 4\) (True)
- This set can form a triangle.

3. **4, 4, 7**
- \(4 + 4 > 7\) (False)
- \(4 + 7 > 4\) (True)
- \(4 + 7 > 4\) (True)
- This set cannot form a triangle.

4. **4, 4, 8**
- \(4 + 4 > 8\) (False)
- \(4 + 8 > 4\) (True)
- \(4 + 8 > 4\) (True)
- This set cannot form a triangle.

Therefore, the side measures that do not form a triangle are:

- **4, 4, 7**
- **4, 4, 8**