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

A(△DBC) = A(△EBC) Given
Both the triangles have a common base BC.
∴ Their heights are equal.
Since both the triangles have a common base and their heights are equal, the distance between points B, D and distance between points C, E is equal.
Hence, DE || BC.