In Fig. 9.24, ABC and ABD are two triangles on the same base AB. If line- segment CD is bisected by AB at O, show that: ar(ABC) = ar(ABD).

Solution:

In ΔABC, AO is the median. (CD is bisected by AB at O)

∴ar(AOC) = ar(AOD) — (i)

also,

ΔBCD, BO is the median. (CD is bisected by AB at O)

∴ar(BOC) = ar(BOD) — (ii)

Adding (i) and (ii),

We get,

ar(AOC)+ar(BOC) = ar(AOD)+ar(BOD)

⇒ar(ABC) = ar(ABD)