 Hello and welcome to another problem-solving session on triangles in this question. It's given that triangle POS P O P O S and R O Q R O Q are similar. You have to prove that P S this line P S is parallel to Q R Q R. Okay So should be very simple We have to prove that the lines are parallel and we know that two lines are parallel when alternate interior angles are equal So if I somehow prove that angle one is equal to angle two then my job is done and exactly what is Is to be done here, right? So let's try to prove that the two Angles are equal. Okay, how to prove that so it's given so first. Let's write what is given? So given is triangle POS POS is similar to triangle R O Q. Correct? The moment this is given by the Condition of similarity. We know that the angles will be equal corresponding angles will be equal to prove What do we need to prove? We need to prove that P S is parallel to Q R Okay, how to prove that? So let's see the solution or the proof. So what I'm going to do is I am going to write triangle POS what is given is similar to triangle R O Q This is given therefore therefore by the By the conditions of by the conditions of similar triangles of similar triangles We can write Corresponding angles are equal. So hence angle one is equal to angle Q that is to write so angle P So angle S is equal to angle Q. It is very clear from this This is this correspondence over here. So angle S is equal to angle Q. So this implies that alternate Alternate interior Angles Alternate interior angles or that is angle PSO and angle R Q O are equal are Equal are equal and hence and hence we can say and hence We can say PS is Parallel to R Q Correct, you could have done this by proving the other two pairs of angle equal So let's say angle three is also equal to angle four. This is also it can be used This also can be used to prove that PS is parallel to Q R. Correct. I hope you got how to solve such questions