Question

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

Explanation:

Step1: Recall Triangle Inequality

The triangle inequality theorem states that for three segments to form a triangle, the sum of the lengths of any two sides must be greater than the length of the remaining side. So, for sides \(AC\), \(CB\), and \(AB\), the three inequalities are:
\(AC + CB>AB\),
\(AC + AB>CB\),
\(CB + AB>AC\).

If any of these inequalities is not satisfied (i.e., the sum is less than or equal to the third side), the segments cannot form a triangle.

Step2: Analyze Each Option

• Option 1: \(AC + AB>CB\) – This satisfies the triangle inequality (sum of two sides greater than the third), so it doesn't explain why they can't form a triangle.
• Option 2: \(AC + CB
• Option 3: \(AC + CB>AB\) – This satisfies the triangle inequality, so it doesn't explain why they can't form a triangle.
• Option 4: \(AC + AB

Answer:

B. \(AC + CB < AB\)