In Figure, E is any point on median AD of a \(\triangle{ABC}\). Show that ar (ABE) = ar (ACE)

Given,
AD is median of \(\triangle \) ABC.

\(\therefore \) it will divide \(\triangle \)ABC into two triangles of equal area.

\(\therefore \) ar(ABD) = ar(ACD) .....(i)

also,

ED is the median of \(\triangle \)ABC.

\(\therefore \) ar(EBD) = ar(ECD) — (ii)

Subtracting (ii) from (i),

ar(ABD) – ar(EBD) = ar(ACD) – ar(ECD)

\(\Rightarrow \) ar(ABE) = ar(ACE)