 Hello friends welcome again to this session on lines and angles and now we are moving ahead with a few properties around two parallel lines and a transversal now here in this given construct AB is parallel to CD okay there are two coplanar parallel lines and LM is transversal okay transversal now you know what all are the corresponding angles so angle one and angle let's say let me name this as one two three and four let's say this is five six seven and eight so there are four pairs of corresponding angles okay what all so I'm writing corresponding corresponding angles pairs what all are there what all are there so angle one and angle five pair number one angle two and angle six pair number two angle three and angle seven pair number three and angle four and angle eight pair number four so what does this corresponding angle axioms say axioms is if a transversal transversal intersects intersects two parallel lines okay if if treatment is there so then what will happen then then each pair of corresponding corresponding angles are equal this is interesting so corresponding angles are equal if the lines are parallel okay so what do we mean we mean angle one is equal to angle five angle two is equal to angle six angle three is equal to angle seven and angle four is equal to angle eight now this is an axiom guys so we can't really figure out a proof for this okay so this is a statement by observation by experiments we have seen that angle one is always equal to angle five two is equal to six three equal to seven four equals to eight only when two lines are parallel okay so this is a important property now not only this is this particular statement is true its converse is also true so what is its converse let's understand that so converse converse of this what is that we say if any pair now all the four need not be right right if any pair all the four pairs we don't need to check so if any pair of corresponding corresponding angles are equal equal when a transversal intersects or cuts two lines then the lines are parallel lines are parallel this is converse this is also true this is also an axiom okay so what do we mean so one let's say there are two lines given and you don't know whether they are parallel or not let's say there are two lines like that okay and you draw a corresponding you know a transversal you simply draw a transversal and you figure out that this angle one is equal to this angle two let's say so if angle one is equal to angle two then then if if angle one is equal to angle two then let's say this line is l and m so l is parallel to m right so in the in the first case in the first axiom we are saying if the lines are parallel then the corresponding angles are equal and in the second case we are saying if the corresponding angles are equal then lines are parallel okay so hence it is called the converse and both are axioms okay so using this axiom we are going to prove many other theorems which are going to be there in the subsequent sessions