Question

Identify the side measures that will not form a triangle
Two, two, one
Three, three, six
Three, three, four
Two, two, two

Answer 1

To determine whether a set of three side lengths can form a triangle, we use 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 analyze each set of side measures:

1. **Two, two, one**:
- \(2 + 2 > 1\) → True
- \(2 + 1 > 2\) → True
- \(2 + 1 > 2\) → True
This set can form a triangle.

2. **Three, three, six**:
- \(3 + 3 > 6\) → False
- \(3 + 6 > 3\) → True
- \(3 + 6 > 3\) → True
Since one of the inequalities is false, this set cannot form a triangle.

3. **Three, three, four**:
- \(3 + 3 > 4\) → True
- \(3 + 4 > 3\) → True
- \(3 + 4 > 3\) → True
This set can form a triangle.

4. **Two, two, two**:
- \(2 + 2 > 2\) → True
- \(2 + 2 > 2\) → True
- \(2 + 2 > 2\) → True
This set can form a triangle.

In summary, the set of side measures that will not form a triangle is:
- **Three, three, six**.