Question

In the adjoining figure, AD is a median of $\Delta ABC$ and DE || BA. Show that BE is also a median of $\Delta ABC$.

Answer 1

ANSWER:
AD is a median of ∆ ABC.
∴ BD = DC
We know that the line drawn through the midpoint of one side of a triangle and parallel to another side bisects
the third side.
Here, in ∆ ABC, D is the mid point of BC and DE || BA (given). Then DE bisects AC.
i.e., AE = EC
∴ E is the midpoint of AC .
⇒ BE is the median of ∆ ABC.