 So we have to prove EF is parallel to BC So whenever we see that there is something parallel to be proven then we can get a hint that you know We can use basic proportionality theorem and it's converse So let's see if we can use this here now first We will use the angle bisector theorem because it's given that DE and DF are angle bisector So that will help us in finding out the ratios of the divided sides Is it it? So let's approach like that So Let's begin the proof So Let's prove it now. You can say in triangle in triangle adb adb We can write ae by eb is equal to ad By bd and why is that? This is because angle bisector theorem correct angle bisector theorem where DE is the bisector, isn't it? DE is the Bisector no doubts about it. D is the bisector of triangle or sorry angle adb, okay? similarly Similarly, so I'm writing similarly similarly in triangle in Triangle what a dc a dc Okay, adc. What can we say in triangle adc? We can say A f by fc a f by fc is equal to ad upon dc same theorem Same theorem, isn't it? Right? So let it be one and Let it be two. Okay. Now since Since ad is the Median So when a median is there, what does it mean? It means Bd is equal to dc Okay, bd is equal to dc. Therefore From one and let's say this is three So from one and three what do we get? We can replace this bd here By dc, isn't it? So hence we'll get a e by eb is equal to ad by ad by and Instead of bd here instead of bd. I can write dc This is let's say four Now if you notice two and four so from two and Four the RHS of both are same. So hence we can say a f by fc is equal to a e by eb Right a f by fc is equal to a e by eb. Now. Let's go to the figure. So a f by a f by fc What is a f and fc? Let's see. So this is a f by fc. So a f by fc is equal to a e by eb So what does it indicate it it hints towards converse of Bpt, isn't it? So hence we can say by by converse of Basic proportionality theorem. What do we get? Ef is parallel to bc Right. This is what We had to prove And we got it. Okay. So what is the learning? learning in this So always try to see from, you know, the Target or the objective and come backwards to the problem, right? So you can always keep the objective in mind Objective that is in this case you have to prove parallel. So from there you got the hint objective will get the hint correct and You know travel back Travel back means come from the objective. So treat the objective to be true and try to establish that the given facts which is there You know or basically from objective come back to the given fact if you are getting a route like that Then you can reverse the route and find the objective, right? So this could be a learning This could be a trick to solve proving problems