 Hello and welcome to the session. Let us solve the following question which says p and q are any two points lying on the sides dc and ad respectively of a parallelogram a, b, c, d. Show that area of a, p, b is equal to area of b, q, c. So, before solving this problem let us first learn a simple property which says if a triangle and a parallelogram are on the same base and between the same parallel lines area of triangle equal to the area of parallelogram. So, this is the key idea with the help of which we are going to solve the given problem. So, first let us solve this property. So, here we are given that the triangle and the parallelogram are on the same base and between the same parallel lines. So, let a, b, c, d be the parallelogram which is on the base dc and the triangle on the base dc we have and let the perpendicular distance between the parallel lines be equal to h and let this point be denoted by e. Now, as we know area of triangle is half base into height. So, here the area of triangle d, e, c will be half into basis dc and height is the perpendicular distance between the two parallel lines a, b and dc. So, this is equal to h and this is further equal to half into area of parallelogram a, b, c, d. Since area of a parallelogram is the base into corresponding altitude therefore, we have dc into h is equal to area of parallelogram and thus we have proved that area of triangle d, e, c is equal to half area of parallelogram a, b, c, d. Now, let us try to show that area of triangle a, p, b is equal to area of triangle b, q, c. So, first let us interpret the given question in the form of a figure. Here we are given two points p and q on the side dc and ad of a parallelogram a, b, c, d. So, the rough figure will be like this in which p and q are two points on the side dc and ad and we have to show that area of triangle b, q, c which is this triangle is equal to area of triangle a, b, p which is this triangle. Fine. Let us now start. First let us write down what we are given. So, we are given a parallelogram a, b, c, d in which points p and q lies on side dc and ad respectively and we have to show that area of triangle a, p, b is equal to area of triangle b, q, c. Now, since a, p, c, d is a parallelogram. So, this implies a, p is parallel to c, d and ad is parallel to b, c. Since opposite sides of a parallelogram are parallel. Now, from our key idea we can write that area of triangle a, p, b is equal to half area of parallelogram a, b, c, d. Since triangle a, p, b lies on the base a, b and is between the parallel lines a, b and c, d and also the parallelogram a, b, c, d is on the base a, b and between the same parallel lines. Therefore, by our key idea this implies that area of triangle is half area of parallelogram. So, let this be equation number one. Similarly, if we consider this side which is the base of triangle b, q, c we can say that area of triangle b, q, c is half area of the same parallelogram which is a, b, c, d. Now, from one and two, on comparing we find that right hand side of both the equations is same. So, this implies that left hand side is also same. That is area of triangle a, p, b is equal to area of triangle b, q, c. So, thus we have proved that area of triangle a, p, b is equal to area of triangle b, q, c. So, this completes the session. Take care and have a good day.