The Total solution for NCERT class 6-12
In Fig.9.23, E is any point on median AD of a ΔABC. Show that ar (ABE)= ar(ACE).
Given,
AD is median of ΔABC. ∴, it will divide ΔABC into two triangles ofequal area.
∴ar(ABD) = ar(ACD) —(i)
also,
ED is the median ofΔABC.
∴ar(EBD) = ar(ECD) —(ii)
Subtracting (ii) from(i),
ar(ABD) – ar(EBD) =ar(ACD) – ar(ECD)
⇒ar(ABE) = ar(ACE)