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  • 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) equals ar (ABD).

Q : 4    In Fig. \small 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  \small ar(ABC)=ar(ABD).

                

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We have, \DeltaABC and \DeltaABD on the same base AB. CD is bisected by AB at point O.
\therefore OC = OD
Now, in \DeltaACD, AO is median
\therefore ar (\DeltaAOC) = ar (\DeltaAOD)..........(i)

Similarly, in \DeltaBCD, BO is the median
\therefore ar (\DeltaBOC) = ar (\DeltaBOD)............(ii)

Adding equation (i) and eq (ii), we get

ar (\DeltaAOC) + ar (\DeltaBOC) =  ar (\DeltaAOD) + ar (\DeltaBOD)

\small ar(ABC)=ar(ABD)

Hence proved.

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manish

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