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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 `ar(triangleABC)=ar(triangleABD)`

Text Solution

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As `CD` is bisected by `AB` at `O`, it means,
`AO` is the median of triangle `ACD` and `BO` is the median of triangle `BCD`.
As median divides a triangle into two triangles with the same area.
`ar(AOC) = ar(AOD)` and `ar(BOC) = ar(BOD)`
So,`ar(AOC)+ar(BOC) = ar(AOD)+ar(BOD)`
`ar(ABC) = ar(ABD)`
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