$A M$ is a median of a triangle $A B C$ . Is $A B + B C + C A > 2 A M$ ? (Consider the sides of triangles $△ A B M$ and $△ A M C$ . )

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Solution

We know,
In a triangle sum of two sides is greater than the third side
Hence,In triangle ABM
AB + BM > AM .........1
Also in triangle ACM
AC + MC > AM ..........2
Adding equation 1 and 2 we get,
AB + BM + AC + MC > AM + AM
AB + AC + (BM + MC) > 2AM
AB + AC + BC > 2AM

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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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