The Total solution for NCERT class 6-12
In Fig. 9.24, ABC and ABD are two triangles on the same base AB. Ifline- segment CD is bisected by AB at O, show that: ar(ABC) = ar(ABD).
In ΔABC, AO is themedian. (CD is bisected by AB at O)
∴ar(AOC) = ar(AOD) —(i)
also,
ΔBCD, BO is themedian. (CD is bisected by AB at O)
∴ar(BOC) = ar(BOD) —(ii)
Adding (i) and (ii),
We get,
ar(AOC)+ar(BOC) =ar(AOD)+ar(BOD)