Question

In Fig. 9.24, ABC and ABD are two triangles on
the same base AB. If line-segment CD is bisected
by AB at 0, show that ar(ABC)=ar (ABD).​

Answer 1

Answer:

In triangle ABC, AO is the median (CD is bisected by AB at O)

So, ar(AOC)=ar(AOD)..........(i)

Also,

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

So, ar(BOC) = ar(BOD)..........(ii)

Adding (i) and (ii),

We get,

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

⇒ ar(ABC) = ar(ABD)

Hence showed.