Question

Identify the side measures that will not form a triangle
Four, four, eight
Four, four, six
Four, four, seven
Four, four, five

Answer 1

To determine whether three sides can form a triangle, we can use the triangle inequality theorem. This theorem states that for any three lengths \( a \), \( b \), and \( c \), the following conditions must be met:

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

Let's analyze each of the sets of side measures given:

1. **Four, Four, Eight**:
- \( 4 + 4 > 8 \) (False, since 8 is not greater than 8)
- This set cannot form a triangle.

2. **Four, Four, Six**:
- \( 4 + 4 > 6 \) (True, since 8 > 6)
- \( 4 + 6 > 4 \) (True, since 10 > 4)
- \( 4 + 6 > 4 \) (True, since 10 > 4)
- This set can form a triangle.

3. **Four, Four, Seven**:
- \( 4 + 4 > 7 \) (True, since 8 > 7)
- \( 4 + 7 > 4 \) (True, since 11 > 4)
- \( 4 + 7 > 4 \) (True, since 11 > 4)
- This set can form a triangle.

4. **Four, Four, Five**:
- \( 4 + 4 > 5 \) (True, since 8 > 5)
- \( 4 + 5 > 4 \) (True, since 9 > 4)
- \( 4 + 5 > 4 \) (True, since 9 > 4)
- This set can form a triangle.

### Conclusion:
The only side measures that do not form a triangle are **Four, Four, Eight**.