D and E are points on sides AB and AC respectively of $△ A B C$ such that $a r (△ B C D) = a r (△ B C E)$ .Prove that DE||BC.

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Solution

ar(∆BCD) = ar(∆BCE) (Given)
We know, triangles on the same base and having equal areas lie between the same parallels.
Thus, DE || BC.

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