Question

$M$ is a point on side $BC$ of a triangle $ABC$ such that $AM$ is the bisector of $\angle BAC$. It is true to say that perimeter of the triangle is greater than $2AM$? Give reason for your answer.

Answer 1

As long as point $M$M is on line $BC$,BC, the perimeter of $△ABC$△ABC would be greater than $2AM$.2AM.

The sum of the two sides of a triangle is always greater that the third side.

In $△ABM$

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

In $△ACM$,

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

Now, adding equation (1) and (2),

$AB+BM+AC+CM>AM+AM$

$AB+AC+BC>2AM$

Hence, the perimeter of $△ABC$ is greater than $2AM$.