Question

Ant
3. In the figure, AABC and AABD are two
triangles on the same base AB. If line
segment CD is bisected by AB at 0, show
that
ar (AABC)=ar (AABD).​

Answer 1

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)+ar(BOD)

⇒ ar(ABC) = ar(ABD)

Hence showed.