Question

In triangle ABC ,AD is median . A line through D and parallel to AB , meet AC at E .prove that BE is the median of triangle ABC

Answer 1

in ABC D is mid point and DE is parallel to AB with converse of mid point thereom E is mid point of AC

Answer 2

since AD is the median of triangle ABC,then BD=DC
given,DE is parallel to AB and DE is drawn from the mid pont of BC i.e D,then by converse of mid point theorem ,
it bisects the third side which in this case is AC at E.
therefore,E is the mid point of AC.
hence,BE us the median of triangle ABC.
hope you understand it