232k views
1 vote
Which inequality can be used to explain why these three segments cannot be used to construct a triangle? AC + AB > CB AC + CB < AB AC + CB > AB AC + AB < CB

User Greg Lyon
by
7.9k points

2 Answers

2 votes

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.

User Panos Boc
by
8.4k points
7 votes

The answer is gonna have to be B.

User Reed
by
8.0k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.