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