which inequality can be used to explain why these three segments cannot be used to construct a triangle? ac…

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

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

Answer

Explanation:

Step1: Recall triangle - inequality theorem

The sum of the lengths of any two sides of a triangle must be greater than the length of the third side. If this condition is not met, a triangle cannot be formed.

Step2: Analyze each option

  • Option 1: (AC + AB>CB) satisfies the triangle - inequality theorem and allows for triangle formation.
  • Option 2: (AC + CB<AB) violates the triangle - inequality theorem. If the sum of two side - lengths ((AC) and (CB)) is less than the length of the third side ((AB)), the segments cannot form a triangle.
  • Option 3: (AC + CB>AB) satisfies the triangle - inequality theorem and allows for triangle formation.
  • Option 4: (AC + AB<CB) violates the triangle - inequality theorem, but we need to find the one that best explains the non - formation based on the given segments' relationship. In the context of the problem, (AC + CB<AB) is the key non - triangle condition.

Answer:

B. (AC + CB<AB)