 Welcome friends again back to our theorems, and we are now going to prove another one In this case, it's given that if a transversal intersects two parallel lines the bisectors of any two corresponding angles are parallel. Okay, so what's given guys? so given is a b is parallel to CD and Pq is the transversal transversal Okay, so lots of such transversals, you know in this last three four sessions never mind. It is going to help us build our foundation. Okay, Pq is the transversal and rp bisects angle prb angle prb and su bisects angle PSD okay, or rsd whichever way you want to say right So what do you do? What do you need to prove to prove? What do you need to prove is? RT is Parallel so you need to prove that RT is parallel to su. Okay, so let's begin the proof So What do we need to do? So we know that AB is parallel to CD. So hence we can say since AB is parallel to CD. You can say angle prb is equal to angle PSD and they are corresponding angles Corresponding Angles isn't it? So this is done. That means if I divide that These these two angles by two both sides. It will be same PSD by two Now clearly, what is PRB by two so you can see Angle PRB by two is nothing but angle PRP Isn't it because RT divides this line divides PRB so angle PRT is half of PRB Okay, and half of PSD if you see is nothing but angle PSU Right, so I'm talking about these two angles. So first angle is this one and The second angle is this one. So if you see RT could be you know produced backwards So let's say this is RT dash and SU you can produce backwards like that So these are the two lines now Let's say you you dash and T dash T and clearly PQ is the transversal where PRT is equal to PSU. So what do we see from here? It looks like they are pair of corresponding angles themselves. So hence they are these these are angles. They are They are corresponding corresponding angles Okay, and corresponding angles are equal that means T dash T is Parallel to U dash U or RT is parallel to SU Correct, this is what We needed to prove so the bisectors of the corresponding angles RT and SU themselves are parallel. Okay, hence proved