In 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(ABC) = ar (ABD).
Solution:
We need to show that
It is given that OC=OD. It means that AO is the median of
. Also, BO is the median of
.
(1)
(Median of a triangle divides it into two triangles of equal areas.)
And,
(2)
(Median of a triangle divides it into two triangles of equal areas.)
Adding (1) and (2), we get
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