Question

$AM$ is a median of a triangle $ABC$. Is $AB+BC+CA>2AM$?
(Consider the sides of triangles $\Delta ABMand\Delta AMC$)

• A. True
• B. False

Answer 1

The correct option is A True

The sum of measures of any two sides of the triangle is greater than the third side.

So, In triangle $ABM$

$AB+BM>AM$ ..................... (1)

In triangle $AMC$

$MC+AC>AM$ ...................... (2)

Add (1) and (2),

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

$AB+BC+AC>2AM$

So, the statement is true.