Question

In Δ ABC, AD is the median and DE is parallel to BA, where E is a point in AC. Prove that BE is also a median.

Answer 1

Since AD is the median of ΔABC, then BD = DC.

Given, DE || AB and DE are drawn from the midpoint of BC i.e. D, then

by the 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 is the median of ΔABC.