 Hello friends welcome again to another session on triangles as you know we are Discussing similarity criteria of two triangles. So in this session, we are going to take up SSS similarity criterion Now as the practice has been we will first try and validate The particular condition or the criterion and in the next video, we are going to take up the proof as well Okay, so before we take up any proof We must see using any tool possible to and validate whether whatever is being said is actually true So if it appears that yes the results appear to be true then we go and try and prove the particular result or the given criterion, right? So in this session, we are going to take up SSS similarity criterion Which says that if two triangles are given and the corresponding site ratios are all equal Then the two triangles are similar. I'm repeating once again So if two triangles are given and their corresponding site ratios are equal Then the triangles are similar. Now, we know that to prove any two Geometric figure to be similar. We need to establish two criteria One is that all the angles must be equal corresponding angles must be equal and all the sides are all the corresponding sides must be Proportional. These are the two criteria we have learned and in triangles We also learned that the either of the two criteria is sufficient enough to prove that the two triangles as of you know congruent and in that league we are now trying to prove that if Only we know that the two corresponding sites that is AB upon EF and BC upon FG and CA upon GE These three ratios are equal which otherwise mean that if the sides that is corresponding sides are proportional Then automatically the corresponding angles are also going to be equal. That's what we are going to prove here Right or first we'll validate and then we'll see whether we can prove that or not Okay, so this is the criterion once again if the corresponding sides are proportional So EG AC are you know corresponding sides EF AB are corresponding sides and FG and BC are Corresponding sides. So if I take their ratios One by one and if all these ratios are equal then automatically it will mean that angle E will be equal to angle A Angle F will be equal to angle B and angle G is equal to angle C Okay, in this case So what I have tried to demonstrate over here is there are two triangles which I have drawn which I have constructed using this Geo-Jibra tool and what I have also done is I have found out the Lengths of each side for example AB if you see is 3.61 units in this case BC is 6 CA is 5 Okay, similarly EF is 6.32 FG is 10.52 and GE is 8.76 and then I have Calculated the ratios corresponding sides ratios what we are going to do is we are first going to move this point E so that we get different configurations of these two triangles and We will make sure that the ratios are same the corresponding ratios here, whatever we have found out Are same and then we'll try and see whether the angles Appear or they actually come out to be equal. So let's do that. So I'm what I'm going to do is I am moving this point E and you can see all the ratios are Changing all the ratios are changing, but they are constant. They are same ratios are changing but All are equal point three one point three one point three one here the ratio is AB this upon EF right as I go on the other side You can see the ratios are increasing and eventually eventually it will become like that So this is also Triangle where the ratios are being maintained and hence we'll see that the angles are indeed equal, right? So let us stop somewhere. So let us stop here Okay, where the ratios are point four one each now Let's try and measure the angles of these two triangles. Okay, so this is how it is done So I'm first measuring angle E. Let's measure angle E. So this is eighty six point eight two So hence we should get the same angle here. The angle a is corresponding. So let's see Yes, so first angle is equal Okay, so E is equal to a okay now. Let's measure F so This is angle F 56 point three one and let's try and measure B should come the same and Indeed it is coming the same. So two angles are correspondingly equal and it goes without saying that third will be same right and Righty, so you can see right. So all the three angles corresponding angles alpha is equal to beta here Dama is equal to delta here and epsilon is equal to jeta here. So all the three angles corresponding angles are Equal fantastic. So now what I'm going to do is going to again change the location of E That means I'm going to change the configuration of the two triangles and see whether The angles as well as the ratios are same and you can verify at this location again the angles have not been you know altered and the ratios are Different but equal in the sense the values are different. But now They're equal and you can see here. Also, this is correspondence, right? But E is corresponding to a F is corresponding to B and G is corresponding to C So even if look-wise they do not appear to be similar, but actually They are similar, right? So hence you can get any such configuration Angles are always going to be the same if the ratios are same So that's what we wanted to establish in this session in the subsequent session Let's try and prove triple S similarity criterion I hope you understood this particular or you could get some sense of this particular validation