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Question

In the figure, ABC and ABD are two triangles on the base AB. If line segment CD is bisected by AB at O, show that ar (ABC)=ar(ABD)

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Solution

Given : in the figure, ABC and ABD are on he same base AB and line CD is bisected by AB at O. Hence, CO = OD.
To prove : ar(ABC)=ar(ABD)
Construction : Draw CLABandDMAB


Proof : In CLOandEMOL=MCO=ODCOL=DOMCLODMO
CL=DM (By CPCT)
Now ar (ABC)=12Base×Height=12×AB×CLand ar (ADB)=12×AB×DM=12AB×CL


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