 Hi, and welcome to the session. Let us discuss the following question. The question says, A, B, C, D, is it a P, C, M, with A, B, parallel to B, C. A line parallel to A, C intersects A, B, F, and X, and B, C, F, Y. Proof that area of A, D, X is equal to area of A, C, Y. Let's start making a feather to understand this question. A, B, C, D, is it a P, C, M, with A, B, parallel to B, C. A line parallel to A, C. Let's now draw a line parallel to A, C. Intersects A, B, and X, and B, C, and Y. Right. We have to prove that area of A, D, X, let's now join D, X is equal to area of A, C, Y. Let's now join A, Y. We will also join C, X. Let's now write down the given information. Now it is given to us that A, B, C, D is a trapezium, is parallel to D, C, is parallel to A, C. Because it is given that a line parallel to A, C intersects A, B, and X, and B, C, and Y, so line X, Y is parallel to A, C. Now in construction, we have joined C, X. Let's now begin the proof. Consider triangle A, C, Y and triangle A, C, X. Triangle A, C, Y between triangle A, C, Y is equal to area of triangle A, C, X. So A, C is equal to given in your book with stable in area. Same this equation as equation number one. The question we are given that A, B is parallel to D, C. Now as A, B is parallel to D, C, so this means part of A, B, that is A, X will also be parallel to D, C. Right. So A, B parallel to D, C implies A, X is parallel to D, C. Now consider triangle A, D, X and triangle A, C, X. Now since triangle A, C, X and triangle A, D, X are on the same way between the same parallel equal to area of triangle A, D, X by theorem 9.2 given in your book which says that on the same way they are equal in area. Same this equation as equation number one. Sorry, as two. From one we have area of A, C, X is equal to area of A, C, Y. From two we have area of A, C, X is equal to area of A, D, X from one and two. We can conclude that area of A, C, Y is equal to area of A, D, X. We have proof that area of A, C, Y is equal to area of A, D, X. This completes the session. Bye and take care.