 Hi and how are you all today? My name is Priyanka and the question to be discussed says D and E are points on side EB and AC respectively hope angle ABC such that area of DBC is equal to area of EBC. Prove that DE is parallel to BC. Now this is the figure that we need to refer. Now here we are given in the question that area of DBC that is this area is equal to EB that means this area and we can see that this portion is common to both of them right. So let us start with our solution since triangle DBC and triangle EBC are equal in area it's given to us that their areas are equal and have the same base that is BC therefore substitute from E of triangle EBC is equal to substitute E of triangle DBC right this implies altitude will be equal to this altitude let me darken this line then this implies that triangle DBC between the same parallel lines and the altitudes that means they are between the same parallel line and therefore E is parallel to BC right so this was the proof that if for the question that was given to us I hope you understood it well take care and bye for now.