 Hello students. Welcome to the session. Let us discuss the following question. A and F are points on the sides PQ and PR respectively of a triangle PQR. For each of the following cases, state weather EF is parallel to QR. For the second part, PE is equal to 4 cm, QE is equal to 4.5 cm, EF is equal to 8 cm and RF is equal to 9 cm. First of all, let us understand the converse of basic proportionality theorem. It states that if a line divides two sides of a triangle in the same ratio, then that line is parallel to the third side of the triangle. That is, if in triangle we are given AD upon DB is equal to AE upon EC. Then by converse of basic proportionality theorem, we get DE is parallel to BC. This is the key idea to solve the given question. Let us now start the solution. Now, in triangle PQR, E and F are the points on PQ and PR. We have to find if EF is parallel to QR. So, first of all, we will find out the ratio PE upon ECU. So, we can write PE upon ECU is equal to 4 upon 4.5, which is equal to 8 upon 9. So, we get PE upon ECU is equal to 8 upon 9. Now, we will find the ratio PF upon FR. So, we can write PF upon FR equal to PF is equal to 8 centimeter and RF is equal to 9 centimeter. So, we will write 8 upon 9. Clearly, we can see PE upon ECU is equal to PF upon FR. F is parallel to QR. Since EF is dividing PQ and PR in the same ratio. So, by converse of basic proportionality theorem, we get EF is parallel to QR. So, we can write how our required answer is yes. EF is parallel to QR. This completes the session. Hope you understood the session. Take care and goodbye.