Question

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

Answer 1

Answer:

So, in the triangle ABC. We have sub triangles ABM and AMC.

So, in triangle ABM

Using the inequality of the triangle that the sum of any two sides is always greater than or equal to the third side.

We have AB+BM>AM. …………………… (1)

Also using the same in triangle AMC,

We have AC+MC>AM. ……………………. (2)

Adding equation (1) and (2), We get

AB+AC+(BM+MC)>2AM

=AB+AC+BC>2AM

Hence AB+BC+CA>2AM is proved to be true.

Step-by-step explanation:

Mark as brainliest