How I can proof that a median divides a triangle in two equal half

Let A,B,C be a triangle and median from A is drawn on BC at point D. BD = CD and median AD is common to both the triangle. Now Using sin formula of area of triangle,
Area = (1/.2)AD*BD sin(<ADB) = (1/2)AD*DC*Sin(<pi – <ADB) and these will be equal.

Thanks.