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In Fig. 9.24, ABC and ABD are two trian...

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 ``

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Given, ABC and ABD are two triangle on the same base AB.
The line segment CD is bisected by AB at O. `( .: OC = OD)`
In `DeltaACD`, we have
`OC= OD` (given)
`:. AO` is the median.
Since, the median divides a triangle in two triangles of equal areas.
`:. ar(DeltaAOC) = ar(DeltaAOD)`...(1)
Similarly, in `DeltaBCD, " " ar(DeltaBOC) = ar(DeltaBOD)`...(2)
On adding (1) and (2), we get
`ar(DeltaAOC) + ar(DeltaBOC) = ar(DeltaAOD) + ar(DeltaBOD)`
`rArr ar(DeltaABC) = ar(ABD)`
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