AM is a median of a triangle ABC. Is AB + BC + CA > 2AM? (Consider the sides of triangles ABM and AMC)

We know that,


In a triangle,


The sum of the length of either two sides of the triangle is always greater than the third side


In the given question, we have to show that:


AB + BC + CA > 2 AM


Therefore,


In ABM, we have:


AB + CM > AM (i)


Same is the case with ACM, in which:


AC + CM > AM (ii)


Adding (i) and (ii), we get


AB + BM + MC + AC > AM + AM


AB + BC + AC > 2 AM


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