In Fig.9.23, E is any point on median AD of a ΔABC. Show that ar (ABE) = ar(ACE).

 

Solution:

Given,

AD is median of ΔABC. ∴, it will divide ΔABC into two triangles of equal area.

∴ar(ABD) = ar(ACD) — (i)

also,

ED is the median of ΔABC.

∴ar(EBD) = ar(ECD) — (ii)

Subtracting (ii) from (i),

ar(ABD) – ar(EBD) = ar(ACD) – ar(ECD)

⇒ar(ABE) = ar(ACE)