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# D and E are points on sides AB and AC respectively of $$\triangle{ABC}$$ such that ar (DBC) = ar (EBC). Prove that DE || BC.

$$\because$$ $$\triangle{BCE}$$ and $$\triangle{BCD}$$ are lying on a common base BC and also have equal areas.
$$\therefore$$ $$\triangle{BCE}$$ and $$\triangle{BCD}$$ will lie between the same parallel lines.
$$\Rightarrow$$ DE || BC