AM is a median of a triangle ABC Is AB+BC+AC greater than 2AM ?
(Consider the sides of triangle ABM and triangle AMC .

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Solution

AM is a median of a triangle ABC. Is AB+BC+CA>2AM?

In triangle ABC, AM is a median.

In triangle ABM, AB+BM>AM… (1) [the sum of two sides of a triangle are greater than the third side].

In triangle ACM, AC+CM>AM… (2) [the sum of two sides of a triangle are greater than the third side].

Add (1) and (2) to get

AB+BM+AC+CM>AM+AM, or

AB+(BM+CM)+AC>2AM, or

AB+BC+CA>2AM. Proved

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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.)

AM is a median of a triangle ABC.

Is AB + BC + CA > 2 AM?

(Consider the sides of triangles ΔABM and ΔAMC.)

If AM is a median of triangle ABC. Then AB +BC +CA $>$ 2AM

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