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AM is a median of triangle ABC. Which statement is true?

Class 7Triangle InequalityTriangles
  • AAB + BC + CA > 2AM
  • BAB + AC = 2AM
  • CAB + BC + CA < AM
  • DBC > AB + AC

Step-by-Step Solution

In triangle ABM: AB + BM > AM. In triangle ACM: AC + CM > AM. Adding: AB + AC + (BM + CM) > 2AM, and BM + CM = BC. So AB + BC + CA > 2AM.
Answer: A) AB + BC + CA > 2AM

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