Question

# Question 4 In the given 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).

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Solution

## Consider ΔACD. Line-segment CD is bisected by AB at O. Therefore, AO is the median of ΔACD. ∴Area(ΔACO)=Area(ΔADO)...(1) Considering ΔBCD,BO is the median. ∴Area(ΔBCO)=Area(ΔBDO)...(2) Adding equations(1) and (2), we obtain; Area(ΔACO)+Area(ΔBCO)=Area(ΔADO)+Area(ΔBDO) ⇒Area(ΔABC)=Area(ΔABD)

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