Question

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

Explanation:

The triangle inequality theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the remaining side. Here, the two sides are 7 and 4, and their sum is \(7 + 4 = 11\), which is less than the third side (15). The figure shows that a triangle cannot be formed in this case, which matches option D's description of showing a triangle cannot be formed when the sum of two sides is less than the third side. Options A and C are incorrect because the sum of 7 and 4 is not greater than 15, so "only one triangle" is not formed. Option B is incorrect as the sum is less, not equal, to the third side.

Answer:

D. 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