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

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

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ΔDBC and ΔEBC are on the same base BC and also having equal areas.

∴ they will lie between the same parallel lines.

∴ DE || BC.

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