 Hi and welcome to the session. Let us discuss the following question. Question says in figure 6.18 if Ln is parallel to Cb and Ln is parallel to Cb prove that a m upon a b is equal to a n upon a d. This is the figure 6.18. First of all let us understand basic proportionality theorem. Basic proportionality theorem states that if a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points the other two sides are divided in the same ratio. That is if we are given a triangle abc in which d e is a line parallel to bc, clearly we can see d e is intersecting ab and ac at distinct points d and e. So this line will divide ab and ac in the same ratio. So we can say if in triangle abc d e is parallel to bc then by basic proportionality theorem we get a d upon db is equal to a upon ac. This is the key idea to solve the given question. Let us now start with the solution. Now in figure 6.18 we are given Lm is parallel to bc and Ln is parallel to Cd. So first of all let us consider triangle abc. In triangle abc Lm is parallel to bc or we can say Lm is parallel to Cd. This is given in the question. Now this implies a m upon mv is equal to a l upon lc by basic proportionality theorem. Now let us consider triangle adc. In triangle adc Ln is parallel to Cd. This is given in the question. By basic proportionality theorem we get a n upon n d is equal to a l upon lc. Now in this triangle a n upon n d is equal to a l upon lc and in this triangle m upon mv is equal to a l upon lc. So we get a m upon mv is equal to a n upon n d since both the ratios are equal to a l upon lc. So these two ratios must be equal. Now let us name this expression as 1 and this expression as 2. So from 1 and 2 we get a m upon mv is equal to a n upon n d. Now taking reciprocal of both the ratios we get mv upon m is equal to n d upon n. Now adding 1 on both the sides we get mv upon m plus 1 is equal to n d upon n plus 1. Now we will add these two terms by taking their LCM. We get mv plus m upon m is equal to similarly here we will add these two terms by taking their LCM. So we get mv plus a n upon n on right hand side. Now clearly we can see mv plus m is equal to a b. So we can write a b upon m here this is equal to we know n d plus a n is equal to a d. So on right hand side we can write a d upon a n. Now taking reciprocal of both the ratios we get m upon a b is equal to a n upon a d. This is our required answer. We were required to prove this only. So this completes the session. Hope you understood the session. Take care and have a nice day.