 Hi friends. So in the last sessions, we saw the concept of similarity and what is meant by similarity of polygons Now in the rest of them the series will focus only on similar triangles, you know So one of the polygons triangles, right? And what is meant by similar triangles and how do we establish what are the criteria of similarity? How do we establish those criteria and are there any rules and Laws related to that are their theorems related to that we'll study all of them one by one now Let us start with the concept of similar triangles. So let us say we have two triangles given Okay, let us say this is a B C and another triangle is D E F Okay, so D E F and we say Triangle a b c is similar to triangle D E F now mind you again. I am the the order of these Vertices the way you write is very very critical. You cannot change the order. You must see the correspondence is true So a is equal to be D B is equal to E and C is equal to F Okay, the order will change only when the corresponding angles change For example, if let us say a was equal to E Then obviously you'd have written triangle a b c is trying is similar to triangle E first Why because a is corresponding to E and let us say B was corresponding to D Let us say B is was corresponding to D So you'll then write D and let us see was then equal to F like that So order is very important order determines which two vertices angles are same So a is equal to E in this case B is equal to D and C is equal to F If this was not the case and this was the case then you'd have write you would have written triangle a B C is Similar to triangle D E F now many a times what happens is people get trapped because of the you know The diagram so the diagram may be deceptive So only criteria to establish or when you're doing sums, please make sure that the corresponding Angles must be same and it must be written in the same order Okay, coming to the conditions for similarity of triangles. So what are the criteria criteria is the same what we studied in the last session? criteria for similarity of Triangles Okay, there are two criteria one is corresponding corresponding angles must be equal and second criteria is corresponding sides Must be proportional must be proportional Proportional but thankfully In case of triangles you don't need to establish both of them For any other polygon you need to establish one and two both But for triangles if you establish any one of them the other one is automatically established So if you establish any one of these either one or two then The triangles are similar. What do I mean? Let us say if again there are two triangles a BC and another one is Def Right, so either Either we need to prove or establish one what angle a is equal to angle d and angle b is equal to angle e and Angle c is equal to angle f. This is one or any of the combination corresponding angles must be same or You establish to what is it a b by? De is equal to BC by EF is Equal to C a by Fd Correct if you establish this by this is equal to this by this is equal to this by that then The triangles are similar that is what is Similarity of triangle so you don't need to establish both of them only one is good enough and later You'll see even you know by the properties of triangle You don't need to actually check for all three angles as well if One two of them two of the corresponding angles are equal then third has to be equal automatically by angles some property Which you have learned previously right so even you know these these conditions could be reduced a little further We'll see all of these criteria in the sessions which are following But right now this in this session we now understood what are the criteria for similarity of triangles There are two corresponding angles must be equal corresponding sides must be proportional But in case of only triangles and not any other Polygon even if we establish any one of them that if one of them is established the other one is automatically taken care of So let's begin our discussion on the theorems related to similarity in the succeeding sessions