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 ``

Explanation

As `CD` is bisected by `AB` at `O`, it means,

`AO` is the median of triangle `ACD` and `BO` is the median of triangle `BCD`.

As median divides a triangle into two triangles with the same area.

`ar(AOC) = ar(AOD)` and `ar(BOC) = ar(BOD)`

So,`ar(AOC)+ar(BOC) = ar(AOD)+ar(BOD)`

`ar(ABC) = ar(ABD)`