Suppose D and E are the points on sides AB and AC respectively of ∆ ABC

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

Given, a ∆ ABC and D and E are the points on sides AB and AC respectively, also
ar (DBC) = ar (EBC)
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So, altitude from D of ∆ DBC=altitude from E of ∆EBC
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Hence, ∆ DBC and ∆ EBC are between the same parallels, i.e. DE || BC.