 Hi, and how are you all today? My name is Priyanka. The question says show that the diagonals of a parallelogram divided into four triangles of equal area. Now, this is the figure that we need to refer. Now here the diagonals a, c, and b, d are meeting at point or intersecting at point o and we need to show that the diagonals are dividing this whole parallelogram into four triangles of equal area. So let us start with our solution and write down whatever is given to us. Here we are given that a, b, c, d is a parallelogram and a, c, and b, d are its diagonals. Right? Here we need to prove, we need to prove that the area of all these four triangles are equal. That means area of a, o, b is equal to area of b, o, c is equal to area of c, o, d is equal to area of d, o, a. Right? Now, let us start with our proof. We know that diagonals of a parallelogram bisects each other. That is, o, a will be equal to o, c, o, b is equal to o, d. Right? Also, median of the triangle divides it into two triangles of equal area. Since we know that o, a is equal to o, c, and o, b is equal to o, d, that means o is the median for triangle a, b, d, and d, c, b. Right? So when this is the median of this whole triangle, that signifies that the area of this triangle will be equal to the area of this triangle. So, we can say that, therefore, area of a, o, b is equal to area of a, o, d, because o, a is the median of triangle a, b, d. Similarly, area of triangle b, o, c is equal to area of triangle c, o, d. Now here, o, c is the median of triangle c, b, d. Right? So we have proved that area of triangle d, o, a is equal to area of triangle a, o, b, also area of c, o, b is equal to area of c, o, d. Now, if we can prove that these two areas are also equal, then we can say that all the area of all these four triangles are equal to each other. Also, o, d is the median of triangle a, d, c, isn't it? So what we can conclude by this is exactly, you're right, area of a, o, d is equal to area of c, o, d. So by the first second and third condition, we have area of all these four triangles are equal to each other. That is area of a, o, b is equal to area of b, o, c is equal to area of c, o, d is equal to area of a, o, d. Right? So this was what we were supposed to prove in this question. This ends my session. Hope you enjoy and have a good day.