Question
In a triangle ABC, E is any point on its median AD, show that ar. (ABE) = ar. (ACE).
Solution
Since a median of a Δ divides it into two Δs equal in area. Now, in ΔABC, AD is itsmedian.
∴ ar.(ΔABD) = ar.( ΔACD) …(i)
Now in ΔBEC, ED is the median
∴ ar.(ΔEBD) = ar.(ΔECD) …(ii)
subtracting (ii) from (i) we get
ar. (ΔABD) − ar. (ΔEBD)= ar. (ΔACD) − ar. (ΔECD)
⇒ ar. (ΔABE) = ar. (ΔACE).
