 Hello and welcome to the session. My name is Mansi and I am going to help you with the following question. The question says in figure 8.17, PQ is parallel to AB and PR is parallel to AC. Prove that QR is parallel to BC. So we are given PQ parallel to AB and PR parallel to AC and we have to prove that QR is parallel to BC. So let us start with the solution to this question. Now because PQ is parallel to AB, therefore in triangle AOB, we have AP by PO is equal to BQ by QO or OP by AP is equal to OQ by QB because we see that from the basic proportionality theorem we get that if a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, the other sides are divided in the same ratio that means if a line DE is parallel to BC of triangle ABC then AD by DB is equal to AE by EC. So we have applied this theorem here and we get OP by AP is equal to OQ by QB. We name this one. Again in triangle AOC it's given to us that PR is parallel to AC. Now PR is parallel to AC then again by basic proportionality theorem we have OR by RC is equal to OP by AP. We name this two. Now in one and two we notice that OP by AP is equal to OQ by QB and OR by RC. Therefore from one and two we have OQ by QB that means this by this is equal to OR by RC that means this by this. Now again we see that since this is equal to this therefore QR is parallel to BC that means this is parallel to this. Now we see that this happens because we see that converse of basic proportionality theorem says that if a line divides any two sides of a triangle in the same ratio the line is parallel to the third side that means if in a triangle ABC AD by BD is equal to AE by EC then the line DE is parallel to BC. So using this we get that QR is parallel to BC from converse of basic proportionality theorem hence proved. So I hope that you understood the question and enjoyed the session. Have a good day.