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D and E are points on sides AB and AC r...

D and E are points on sides AB and AC respectively of `DeltaA B C`such that`ar (D B C)\ = a r (E B C)`. Prove that `D E |\| B C`.

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Given: `D` and `E` are points on sides `AB` and `AC` respectively of `ΔABC` such that `ar(/_\DBC)=ar(/_\EBC)`
To prove: `DE∣∣BC`.
Proof: `/_\DBC` and `/_\EBC` are on the same base `BC` and are having equal areas.
Hence, They will lie between the same parallel lines.
`therefore DE||BC`.
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