 Hello students and welcome to the session. My name is Shashi and I'm going to help you to solve the following question. Question is, in figure 6.17, first and second, DE is parallel to BC, 5EC in first part and AD in second part. The given figures for first part and second part are here. First of all, let us understand the basic proportionality theorem. Basic proportionality theorem states that if a line is drawn parallel to one side of a triangle, intersecting the other two sides in the distinct points, then the other two sides are divided in the same ratio. Now, let us take an example to understand the basic proportionality theorem. Let us consider a triangle ABC in which DE is parallel to BC. DE is parallel to BC and it is intersecting AB and D and AC at E. So, clearly we can see it is intersecting the two sides at two distinct points and also it is parallel to BC. So, by basic proportionality theorem, it will divide AB and AC in the same ratio. So, we can write, by basic proportionality theorem, DE upon DB is equal to AE upon EC. This theorem is the key idea to solve the given question. Let us start the solution now. For the first part, clearly we can see DE is parallel to BC as it is given in the question and AD is equal to 1.5 centimeter, DB is equal to 3 centimeter, AE is equal to 1 centimeter. We have to find EC. Now, since DE is parallel to BC and DE is intersecting AB and AC at two distinct points that is DE and E. So, it will divide AB and AC in the same ratio. So, by basic proportionality theorem, we get AD upon DB must be equal to AE upon EC. We can write in triangle ABC DE is parallel to BC. This is given to us. Now, by basic proportionality theorem, we can write AD upon DB is equal to AE upon EC. Now, substituting AD is equal to 1.5 centimeter, DB is equal to 3 centimeter and AE is equal to 1 centimeter. We get 1.5 upon 3 is equal to 1 upon EC. This implies EC is equal to 3 upon 1.5, which is equal to 2. So, we get EC is equal to 2 centimeter. Let us now start the solution for the second part. Now, in second part clearly we can see DE is parallel to BC as it is given in the question. Now, this implies AD upon DB must be equal to AE upon EC by basic proportionality theorem. Since AB and AC are intersected by DE at two distinct points that is DE and E. So, DE will divide AB and AC in the same ratio. So, we can write in triangle ABC DE is parallel to BC given to us. Now, we can write by basic proportionality theorem we get AD upon DB is equal to AE upon EC. Now, we have to find AD. We are given DB is equal to 7.2 centimeter, AE is equal to 1.8 centimeter and EC is equal to 5.4 centimeter. Now, we will substitute the corresponding values of DB, AE and EC in this expression. Now, substituting DB is equal to 7.2 centimeter, AE is equal to 1.8 centimeter and EC is equal to 5.4 centimeter. We get AD upon 7.2 is equal to 1.8 upon 5.4. This implies AD is equal to 7.2 multiplied by 1 upon 3. This implies AD is equal to 2.4 centimeter. Therefore, AD is equal to 2.4 centimeter. So, the required answer for the first part is 2 centimeter and the second part is 2.4 centimeter. This completes the session. Hope you understood the session. Take care and goodbye.