 Hello friends, so in the last session we understood a concept called linear pair and we understood that if Two adjacent angles are there Two adjacent angles are there in such a way that the uncommon arms are in opposite direction Then the two angles form a linear pair. Isn't it now? We are going to prove that if a ray stand on a line Then the sum of the adjacent angle so formed is 180 degrees, okay? So for example, let me just draw a line first So let's say this is a line and a ray stands on this line. Okay, so let's say this is O This point is a this is B and C. So OB is the ray OB is the ray standing on line AC Okay, we have to prove to prove What do we need to prove we need to prove that? Angle A OB plus angle B O C is equal to 180 degrees Okay, this is what is also In short called as linear pair Okay, linear pair Okay, so how do we prove this? So for that we know we have to deal with 180 degrees, but we have one knowledge of Type of an angle called the right angle. Isn't it? What is the right angle? So an angle which is which measures 90 degree. So hence what we do is we construct something So we do some construction. So construction is O D Okay O D perpendicular to AC drawn O D is perpendicular to AC now What can we what can we say about this construct we can say? Angle A O B Plus angle B O C. Okay, this is what we have to prove angle AB plus B O C can be written as angle A O D minus Angle, let's say B O D now this angle if you see this angle A O D A O D, where is A O D 90 degree Minus B O D. B O D is this Okay, so clearly 90 degree minus B O D is A O B Okay Plus angle B O C can be written as Angle C O D plus angle B O D. Isn't it? So this entire angle this hole Can be written as this 90 plus this angle Okay, now simplifying what do you get if you see this minus B O D plus B O D will get cancelled And it is nothing but angle A O D plus angle C O D Now what was angle A O D? Clearly A O D is 90 degrees and C O D is also 90 degrees So hence this is 180 degrees Okay, 180 degrees. So hence we prove that if a ray standing is if a ray stand Stands on a line on a line then the sum of that this angle so formed is 180 degrees, right? So hence we will be using this particular theorem a lot So hence we say a linear pair linear pair is always supplementary Supplementary Isn't it linear pair is always supplementary is what is understood? Okay, so we will be seeing the converse of this theorem. So the converse is also true What is converse of this? That if the sum of adjacent angle is 180 degrees so converse means nothing But you take the second part of the theorem that means some of the adjacent angles is 180 degree then then the uncommon arms Then the uncommon arms are Opposite to each other or that means uncommon arm form a line Okay, that's what we're going to Learn in the next session