How i find the best tricky way for solving the question of class 9th of Areas of Parallelograms and Triangles chapter of class 9th give me the best and easy method for this question no.4 of exercise 9.3 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: ar(ABC) = ar(ABD).
In ΔABC, AO is the median. (CD is bisected by AB at O)
∴ar(AOC) = ar(AOD) — (i)
also,
ΔBCD, BO is the median. (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)
⇒ar(ABC) = ar(ABD)