 Hello and welcome to the session. Let us discuss the following problem. E and F are points on the sides PQ and PR respectively of our triangle PQR. For each of the following cases state whether EF is parallel to QR. For the first part PE is equal to 3.9 cm, EQ is equal to 3 cm, PF is equal to 3.6 cm, F1 is equal to 2.4 cm. First of all let us understand the converse of basic proportionality theorem. Converse of basic proportionality theorem states that if a line divides any two sides of a triangle in the same ratio, then the line is parallel to the third side of the triangle. Let us consider a triangle PQR in which PF is a line intersecting PQ at E and PR at F such that PE upon EQ is equal to PF upon FR. Then by converse of basic proportionality theorem we get EF is parallel to QR. So we can write in triangle PQR E upon EQ is equal to PF upon FR by converse of basic proportionality theorem we get EF is parallel to QR. This EF is dividing PQ and PR in the same ratio so it would be parallel to the third side of the triangle that is QR. Let us now start with the solution. We are given triangle PQR in which EF is a line intersecting PQ at E and PR at F. We have to find if EF is parallel to QR. First of all we will find the ratio PE upon EQ. You know PE is equal to 3.9 centimeter and EQ is equal to 3 centimeter. This implies PE upon EQ is equal to 1.3. Let us now find out the ratio PF upon FR. EF upon FR is equal to 3.6 upon 2.4. We know PF is equal to 3.6 centimeter and FR is equal to 2.4 centimeter. So it is further equal to 3 upon 2. Therefore we get the ratio PF upon FR is equal to 3 upon 2. Clearly we can see 1.3 is not equal to 3 upon 2 so the ratio PE upon EQ is not equal to PF upon FR. EF is the line not dividing PQ and PR in the equal ratio so EF is not parallel to QR. So we can write this implies EF is not parallel to QR. So our required answer is no. EF is not parallel to QR. This completes my session. Hope you understood the session. Take care and good bye.