Prove that median of a triangle divides it into two triangles of same areas

Let ABC be a triangle and AD is a median from vertex A to base BC.

Now,

   …… (1)

   …… (2)

Divide equation (1) and (2), we have,

  …… (3)

Since, D is the midpoint of side BC, so,

DB = DC

So equation (3), becomes,

Hence, a median of a triangle divides it into two triangles of equal area.