 Hello and welcome to the session. In this session we discussed the following question which says triangles ABC and DBC are on the same base BC with vertices A and D on opposite sides of BC such that area of triangle ABC is equal to the area of triangle DBC show that BC bisects AD. Before moving on to the solution, let's recall one theorem which says triangles with equal areas on the same or equal basis have equal altitude. This is the key idea that we use for this question. Let's proceed with the solution now. We are given that triangles ABC and DBC are on the same base BC and we have area of the triangle ABC is equal to the area of the triangle DBC. First of all we do some construction in which we join AD. So we have joined AD and let this point of intersection of AD and BC be point E. Then next we draw AM perpendicular to BC and say DN perpendicular to BC. So this AM is perpendicular to BC and DN is perpendicular to BC. We are supposed to show that BC bisects AD that is AE is equal to AD. From the key idea we have that the triangles with equal areas on the same or equal basis have equal altitudes and we know that we are given triangles ABC and DBC which are on the same base BC and they have equal areas that is we say since triangle ABC and DBC are on the same base BC with equal areas. So their corresponding altitudes are equal. Therefore AM would be equal to DN. Now consider the triangles AEM and DEN in this we already have AM is equal to DN then angle AME is equal to angle DNE and each is equal to 90 degrees since they are the altitudes also angle AEM that is this angle is equal to angle DEN that is this angle since they are the vertically opposite angles. So therefore we conclude that the triangle AEM is congruent to the triangle DEN by AAS congruency criteria. Now that these two triangles are congruent this implies that AE would be equal to DE CPCT that is as they are the corresponding parts of the congruent triangle so they are equal and this is what we were supposed to prove hence we have that BC by 6 AD this completes the session hope you have understood the solution of this question.