Question

In the given figure, ABC is a triangle and AD is the median.

If E is any point on the median AD. Show that: Area of ΔABE = Area of ΔACE.

Answer 1

AD is the median of ΔABC.
Therefore it will divide ΔABC into two triangles of equal areas.
∴ Area(ΔABD) = Area(ΔACD) ….(i)
Similarly, ED is the median of ΔEBC.
∴ Area(DEBD) = Area(DECD) ….(ii)
Subtracting equation (ii) from (i), we have
Area(ΔABD) - Area(ΔEBD) = Area(ΔACD) - Area(ΔECD) 
⇒ Area(ΔABE) = Area(ΔACE).