 Hello students and welcome to the session. Let us discuss the following problem. E and F are points on the sides P2 and PR respectively of a triangle PQR. For each of the following cases state method EF is parallel to QR. PQ is equal to 1.28 centimeter, PR is equal to 2.56 centimeter, PE is equal to 0.18 centimeter and PF is equal to 0.36 centimeter. First of all let us understand the converse of basic proportionality theorem. It states that if a line divides any two sides of a triangle in the same ratio then it is parallel to the third side of the triangle. That is if in triangle ABC, AD upon DB is equal to AL upon EC then by converse of basic proportionality theorem we get DE is parallel to BC. This is the key idea to solve the human question. Let us now start the solution. We have to find if EF is parallel to QR. So first of all we will find the ratio PE upon EQ. For that we will have to find EQ. We know EQ is equal to PQ minus PE. So we can find EQ is equal to PQ minus PE. That is EQ is equal to 1.28 minus 0.18 equal to 1.1 centimeter. So we get EQ is equal to 1.1 centimeter. Now let us find out FR. You know FR is equal to PR minus PF. So we can write FR is equal to PR minus PF. Now substituting the corresponding values for PR and PF that is 2.56 minus 0.36. This is further equal to 2.2 centimeter. So we get FR is equal to 2.2 centimeter. Let us now find out the ratios PE upon EQ and PF upon FR. PE upon EQ is equal to 0.48 upon 1.1 which is further equal to 9 upon 55. So therefore PE upon EQ is equal to 9 upon 55. Now let us find out PF upon FR. We know PF upon FR is equal to 0.36 upon 2.2 which is further equal to 9 upon 55. So therefore PF upon FR is equal to 9 upon 55. Clearly we can see PE upon EQ is equal to PF upon FR since all the ratios are equal to 9 upon 55. So we can write PE upon EQ is equal to PF upon FR. Since PE upon EQ is equal to PF upon FR, therefore PF is parallel to QR by converts of basic proportionality QR. So we can write PF is parallel to QR. Our required answer is yes, PF is parallel to QR. This completes the session. Hope you understood the session. Take care and goodbye.