In the following figure BL=CM prove that AD=is the meadine if triangle ABCD
In triangles LBD and MCD,
∠ BLD=∠ CMD
∠ LDB= ∠ MDC
so, ∠ DBL=∠ DCM
and BL=CM
then, triangle LBD congruent to triangle MCD[ASA]
so, BD=DC [C.P.C.T.]
therefore, AD is a median of triangle ABC
Regards