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

Question:

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

Solution:

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.

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