Question

In Figure, 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).

Answer 1

$\text{In}△ADC,AO\text{is the median. (CD is bisected by AB at O)}$
$\therefore ar\left(AOC\right)=ar\left(AOD\right)—\left(i\right)$
also,
$△BCD,BO\text{is the median. (CD is bisected by AB at O)}$
$\therefore ar\left(BOC\right)=ar\left(BOD\right)—\left(ii\right)$
Adding (i) and (ii),
We get,
ar(AOC)+ar(BOC) = ar(AOD)+ar(BOD)
$\Rightarrow ar\left(ABC\right)=ar\left(ABD\right)$