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D and E are points on sides AB and AC respectively of ∆ ABC such that ar (DBC) = ar (EBC). Prove that DE || BC.

Q : 7     D and E are points on sides AB and AC respectively of  \small \Delta ABC such that  \small ar(DBC)=ar(EBC). Prove that \small DE\parallel BC.
 

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M manish

We have  \Delta ABC and points D and E are on the sides AB and AC such that ar(\DeltaDBC ) = ar (\DeltaEBC)


Since \DeltaDBC and \DeltaEBC are on the same base BC and having the same area.
\therefore They must lie between the same parallels DE and BC
Hence DE || BC

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