 Hello friends, welcome to the session. I am Malkha. Let's discuss the given question. Sites AB and BC and median AB of a triangle ABC are respectively proportional to sides PQ and QR and median PM of triangle PQR. C figure 6.41 show that triangle ABC is similar to triangle PQR. Here is the given figure with triangle ABC and PQR. Now let's start with the solution. Let's start with the solution. We have given that AD is the median of triangle ABC. PM is the median of triangle PQ. We are also given that the sides of the triangle ABC and the median are proportional to the sides and median of the triangle PQR. So this can be written as AB upon PQ equal to BC upon QR equal to AD upon PM. And we have to show that triangle ABC is similar to triangle PQ. Now let's see the proof. Now we all know that the median divide the opposite side is equal past. So this implies that PD, BC or we can say that twice of PD equal to BC. Let this be our first equation and since median divide the opposite side in equal past this implies QM equal to half of QR or we can say that twice of QM equal to QR. Let this be our second equation. Now we are also given that AB upon PQ equal to BC upon QR equal to AD upon PM. So this implies that AB implies AB upon PQ equal to, now we will substitute the value of BC from equation first. That is BC is equal to twice of VD upon QR. We will substitute the value of QR from our equation second where QR is equal to twice of QM equal to AD upon PM. Now we see to cancel out this implies AB upon PQ equal to VD upon QM equal to AD upon PM. Now we can say that therefore by SSS criteria of similarity angle ABD is similar to triangle PQM. So that the two triangles ABD is similar to triangle PQM. Therefore their corresponding angles will be equal that is angle B will be equal to angle Q. So we can say that this implies angle B equal to angle Q. Let this be our third equation. Now in triangle by angle PQ PQ equal to BC upon QR we are already given AB upon PQ equal to BC upon QR we are given with this thing. Angle B equal to angle Q equation. So we can say that therefore by criteria of similarity triangle ABC is similar to triangle PQM. So hopefully you understood the solution and enjoyed the session. Goodbye and take care.