AM is a median of a triangle ABC.

Is AB + BC + CA > 2 AM?

(Consider the sides of triangles ΔABM and ΔAMC.)

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Solution

In a triangle, the sum of the lengths of either two sides is always greater than the third side.

In ΔABM,

AB + BM > AM (i)

Similarly, in ΔACM,

AC + CM > AM (ii)

Adding equation (i) and (ii),

AB + BM + MC + AC > AM + AM

AB + BC + AC > 2AM

Yes, the given expression is true.

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Question 3
AM is a median of a triangle ABC. Is AB + BC + CA > 2AM? (Consider the sides of triangles ABM and AMC.)

Δ

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