Question

select the correct answer. how does the figure help verify the triangle inequality theorem? a. by showing that a triangle cannot be formed when the sum of the lengths of two sides is less than the length of the third side b. by showing that only one triangle can be formed when the sum of the lengths of two sides equals the length of the third c. by showing that a triangle cannot be formed when the sum of the lengths of two sides equals the length of the third d. by showing that only one triangle can be formed when the sum of the lengths of two sides is less than the length of the third

Explanation:

Step1: Recall Triangle Inequality

The triangle inequality theorem states that for a triangle with side lengths \(a\), \(b\), and \(c\), the sum of any two sides must be greater than the third side (\(a + b>c\), \(a + c>b\), \(b + c>a\)). If the sum of two sides is less than the third, a triangle cannot be formed.

Step2: Analyze the Figure

The figure shows two segments with lengths 7 and 4, and a third segment of length 15. Calculate the sum of 7 and 4: \(7 + 4=11\). Now, compare this sum to 15: \(11<15\). This shows that when the sum of two sides (7 and 4) is less than the third side (15), a triangle cannot be formed, which aligns with option A's description.

Answer:

A. by showing that a triangle cannot be formed when the sum of the lengths of two sides is less than the length of the third side