 Hello friends, so welcome again to another session on lines and triangles and having seen different types of angles and Some relations with angles like linear pair and vertically opposite angles Now it's the time to go further deep into it and understand some more properties related to lines and angles Now in this case, we are going to study angles made by a transversal With two lines. Okay, that means first of all, we need to understand what is a transversal And what are the properties related to it? So let's say there are two lines a and b on the same plane guys again Please understand. We are talking about two lines in the same plane. Okay, so there could be lines in two different planes as well But we are not going to deal with them. We are going to deal with Only at the case where the two lines are on the same plane or they're also called coplanar lines Lines lying on the same plane are called coplanar lines. So for example, when you take your notebook and Draw any line on any of these pages and draw another line in the same place the same page You will get two coplanar lines. Now, obviously, there is no limit to draw Number of lines on a piece of paper. So all of them are coplanar lines now we have two coplanar lines here a b and CD, okay, and there is another line which intersects The two given lines a b and cd at point p and q Okay, so this line lm if you see is intersecting the two given lines in the same plane Now this line lm is called the transversal trans Versal so it is Starting from one end and then cutting across both the lines Okay, so transversal now attached with transversal or associated with transversal there are few angles and Today in this session, we are going to just define them and in the next session We'll understand the properties of those angles there, you know In some cases for example when a b is parallel to cd So when a b becomes parallel to cd, then all these angles start behaving in a particular way and we'll understand that Okay, so before that let's first understand. So you you understood transversal, right? So lm is transversal to is a transversal Transversal to a b and cd You understood this now What are corresponding angles so here corresponding angles are nothing but angles on the same side of the two lines Okay made by the transversal. What am I saying? Angles made by the two lines or angles made by the transversal on the same side For example, what all here are corresponding angles? So angle one and angle five Okay, angle one and angle five This one and this one why because they are on the same side of both the you know on the left-hand side if you let's say You know or the upper side of both the lines and on the same side of the transversal. Is it it? similarly you can say angle four and angle eight are pair of Corresponding sides again on the downside Downward side of both the lines on and on the right side of the transversal again You know now angle two and angle six are another pair and Angle three and angle seven so these all are pairs of Corresponding angles. Okay, so there are four pairs of corresponding angles basically Now what are alternate interior angles? So Alternate interior angles are these so you have to just look at angles between the two lines now and On the opposite side of the triangles for example see angle three and angle five Okay, so they are on the opposite side of the transversal and They are made between the two lines. Okay angle three and angle five are Alternate interior angles and similarly angle four and angle six are Alternate interior angles. Okay, so on the opposite sides of the transversal such that The two lines form one of the arms of these angles, okay So if you see AB is forming one arm of four and CD is forming one arm one arm of six and Now PQ is the transversal actually is a common arm. Yep. So this is how you can identify Now what are alternate exterior angles similarly to similar to interior? We can have alternate in Exterior so angle one and angle seven Are a pair of alternate exterior angles? Similarly angle two and angle eight are parallel or sorry a pair of Alternate exterior angles. Okay, and what are conjugative interior angles? Now conjugative interior angles are again two angles between the two lines and the same side of the transversal Okay, so hence angle three and angle six are Conjugative interior angles and similarly Angle four and angle five are also corresponding. Sorry consecutive interior angles Okay, so now you understand if there are two lines AB and CD LM is the transversal Angle one angle five are corresponding two and six are corresponding three and seven are corresponding four and eight are corresponding similarly alternate alternate interior angles are This angle and this angle similarly alternate interior angles are this angle and this angle similarly Alternate exterior angles are one and seven and eight and two correct and Conjugative interior angles are Let's say four and five Together and three and six together right these are corresponding. Sorry consecutive interior angle So with this knowledge of you know different angles associated with two co-plural lines and a transversal We will be now moving towards understanding theorems and properties related to this particular construct. Okay. See you in the next session