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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
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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
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7.2k points
7 votes

The answer is gonna have to be B.

User Reed
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