Question

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

Answer 1

Line segment CD is bisected by AB at O (Given)
CO = OD .....(1)
In ΔCAO,
AO is the median. (From (1))
So, arΔCAO = arΔDAO .....(2)
Similarly,
In ΔCBD,
BO is the median (From (1))
So, arΔCBO = arΔDBO .....(3)
From (2) and (3) we have
arΔCAO + arΔCBO = arΔDBO + arΔDAO
$\Rightarrow$ar(ΔABC) = ar(ΔABD)