 Hello friends, so welcome again to another session in the series of lectures We are creating in mathematics today We are going to take up a new topic altogether and that is triangles now before we get into triangles and what exactly we are going to Discuss in this topic. We need to know concept of similarity because if you see in the entire triangle Chapter we are going to discuss, you know similarity mostly so before we plunge into that Let us understand what is concept of similarity? Now the best way to start off any new topic is to deconstruct Let's say the topics and the names which are given so here if you say if you see there is a term similarity right which which originates from the word similar now let us first do a Random Google search on what similar the word similar and similarity mean so here I'm going to you know, just type in the keyword similar and just let's see what do we get as search results So the moment I hit similar I can see So it is saying similar is nothing but having a resemblance in appearance and Character or quantity without being identical. So this is what the dictionary meaning of similar is that is resemblance in appearance is a very important characteristic quantity character or and without being identical that means it is clear that The things must not be same is in you know in exact same size and shape But it should be appearing to be similar, you know similar I think you would see you the word itself is so commonly used that it is becoming so difficult to define this term But let us try one more thing and let us try to search for similar images So what do we get? Oh very good So if you see there are you know a couple of faces which look like same But they're not exactly same in the first figure if you see it says same similar different So similar is different from same. There are apples on the right-hand side here Then there is you know, there are butterflies and things like that. So what do we see we see that One thing is very clear similar is not same Now there is a you know debate where the same can be you know one special case of similar But anyways our our our mandate is to understand similarity in geometry and especially in triangles So let us go back to Our lecture so we saw what does the word similarity or similar mean and when we did a Google search on The word similar also we saw Definitely there are a few things and it said similar in resemblance. So it must appear same appear same, but they're not same resemblance and but they are definitely not identical Not identical, right? So we are now going to study the geometry of similar polygons and especially in this case. We are going to study Similar triangles, okay, so I hope the concept of similarity is clear to you another way of looking at similarity is through the mechanism of scaling scale. So if you have seen a Map, okay, so let us again go and see what Google Maps is Okay, so now this is a map of the world if you can see and here on the Left bottom I will not be able to highlight it on this screen But let us say here on the left hand where it is written map data Copyright 2019 terms and then thousand kilometer. Can you see it's written on the top? I'm sorry left bottom portion of the screen now here thousand kilometer and they have given a dimension also there the length of this particular Thing represents that this much length is thousand kilometers. So if you place the scale here Then that that much scale will be equivalent to thousand kilometers, right? So that this map looks Similar to our world map, but it's actually not the same. Isn't it? It's a scaled-down version of or zoomed out version of Let's say a map. So that's another concept of Similarity, so we have a map which is similar to which it resembles our exact, you know world map so this is another concept of similarity so hence if I Zoom this map in keeps on keep on zooming this map in let us say and then what will happen if I have a fairly large enough screen Equivalent to the let's say the surface area of the earth, then I will be able to coincide At least on a plane the map of the world On to the exact shape of the world So hence similarity you can also see in this way that if you scale up or scale down one of the two figures Which you are comparing then one will you know both of them will be quite coincident after a point in time, right? So you can superimpose one on to the other and you'll see that they are exactly coincident This is another way of looking at similarity. So what we were discussing was let us say You know two circles are definitely similar Isn't it? Why because if you zoom in one circle, let us say this is my one circle So this is one circle and if I this is my second circle other circle So if I if I increase the radius of this second circle, so after some time what will happen? This second circle is going to sit on the first circle exactly. So all circles are all Circles are similar all circles are similar, okay, similarly all Squires are similar, isn't it all squares are similar. Why because because if you zoom in one of these squares And let us say this is another square. So if you zoom in the second one it after some time It will sit on the first one right all squares are similar similarly Similarly, all regular polygons are similar, right all all regular Polygons polygons Are similar why and what is a regular polygon by the way? A regular polygon is nothing but a polygon with Same side length And same value of internal angle. So this is let's say a hexagon A hexagon which is regular regular hexagon means all sides are equal And all the internal angles this angle all these angles must be same, right? Similarly a regular hexagon pentagon and all those regular polygons would be similar then What would be non similar items then non then all Rectangles need not be similar all rectangles Need not be similar. They may be they might not be need not be Need not be similar Okay, for example, you can see your door Door panel and your window panels or your computer screen or your the top surface of The notebook all are rectangles, but they need not be similar Is it Similarly to ellipses need not be similar. For example, if this is one ellipse This is one ellipse and this is Another ellipse these two may not be similar, right? So I hope you understood what is what are similar geometrical figures and what are non-similar figures