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.