Given : ∆ABC in which D and E are points on sides AB and AC respectively, such that BD = CE.To prove : DE || BC.Proof: In ∆ABC, we have∠B = ∠C⇒    AC = AB⇒    AB = AC[Sides opposite equal angles arc equal]⇒    AD + DB = AE + ECBut    BD = CE⇒    AD = AEThus, we have                  AD = AE and BD = CE         Therefore, by converse of Basic proportionality theorem, we get DE || BC.