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

Explanation:

三角形三边关系定理为：三角形任意两边之和大于第三边，任意两边之差小于第三边。图中给出的两边长为\(7\)和\(4\)，它们的和为\(7 + 4 = 11\)，而第三边对应的长度为\(15\)，\(11\lt15\)，即两边之和小于第三边，此时不能构成三角形，这验证了三角形不等式定理中“两边之和小于第三边时不能构成三角形”的内容，对应选项\(C\)。

Answer:

C. 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