Final answer:
To determine if three segments can form a triangle, we apply the Triangle Inequality Theorem. If any inequality stating that the sum of any two segments must be greater than the third is not satisfied, such as AC + AB < CB, then the segments cannot form a triangle.
Step-by-step explanation:
The question asks which inequality can be used to explain why three segments cannot be used to construct a triangle. To determine the possibility of constructing a triangle from three segments, we can use the Triangle Inequality Theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the remaining side.
In this case, for segments AC, AB, and CB to form a triangle, the following inequalities must all be true:
- AC + AB > CB
- AC + CB > AB
- AB + CB > AC
If any of these inequalities is not true, the three segments cannot form a triangle. Therefore, the inequality that explains why these three segments cannot form a triangle is the one that is not satisfied. For example, if
AC + AB < CB
, then these segments cannot form a triangle because the sum of segments AC and AB is not greater than the length of segment CB, which violates the Triangle Inequality Theorem.