 Hello and welcome to the session. In this session we will compare transformations that preserve distance and angle to those that do not. Let us first see the meaning of rigid and non rigid transformations. Now rigid transformations are those transformations that do not change the shape and size of a figure. For example, in translation, we only move the figure to a different position. Its shape and size remains same because it is a rigid transformation plus non rigid transformation. Now these are the transformations which do not preserve size or shape. For example, in dilation figure is either enlarged or contracted like we enlarge a given triangle to form this bigger triangle by dilation. And here the size of the figure is changed thus it is a non rigid transformation. And now let us discuss isometry. Now a transformation of living is the distance between every two points in the original figure as the distance between the corresponding images in the transformed figure. That is mv in the original figure and their respective images mv dash then mv that is distance av equal to distance mv dash that is distance a dash v dash. Now see this figure here a dash v dash c dash d dash e dash f dash is transformed image of the original figure. Now here we can see that distance av is three images that is images of a and b are a dash and v dash respectively. And distance between a dash and b dash is also in their transformed thus the isometry's rigid transformations. Now if any two images are rigid or isometric then and these are also called transformations and sizes are equal thus my transformation reflection and rotation that is the pre image and image after transformation will be rigid and non rigid transformation. Now let us discuss an example. Now here we have to transform the triangle having vertices minus one, one minus one and zero three using even transformations that have distance and which do not. First is given as transform to x plus one, y plus one and second transformation is given as xy transform to these points on the coordinate plane put all the three points on the graph. Now joining these three points we get a triangle. See the first transformation. Now coordinates of vertices in figure are minus. Now according to the first transformation the coordinates of transformed figure that is coordinates of vertices of transformed figure will be zero. Now coordinates of third vertex will be one. You can see that coordinates of first vertex is original figure minus one and then after transformation the coordinates of the first vertex of this transformed figure and minus one plus one that is minus one is zero. Similarly we have got the coordinates of other vertices also. Now let us see this transformation graphically. Now here in the transformed figure we are adding one to the x coordinate and here again we are adding one to the y coordinate. These points as a, b, s we are adding one to the x coordinate. It means vertex a will move one minute to the right. It means they will move one minute to this point. Similarly we obtain v dash with coordinates minus one zero and v dash with coordinates two zero. Now joining all these points we get a triangle a dash v dash c dash. The triangle a dash v dash c dash is the image of the triangle a v c. Now given transformation from here we see that distance a v is equal to dash v dash which is equal to three units. Now here we see that distance b c is equal to distance b dash c dash which is equal to three units a v is equal to distance a dash v dash. Then distance a c is equal to distance a dash c dash. Now here both figures are triangles and having same distance between the points in the image, in the pre-image and also they are having same angles. Thus the given transformation in part one which is a translation preserves distance with the second transformation additional figure minus one and when zero three fix y plus one that is of the transformed figure will be of the form two x y plus one. Now let x be minus two and y be minus one. The coordinates of first vertex of transformed figure will be two into minus two and minus one plus one that is minus four zero. We have called the other vertices that is the coordinates of the vertices on coordinate frame. After this transcend the new English v dash that distance v c is equal to three units that distance v dash c dash is six units. Hence there is a horizontal stretch. The size of triangle has increased is a rigid transformation non-rigid transformation. Thus we see that rigid transformations preserve congruence but non-rigid transformations do not preserve congruence. I have discussed transformations preserving distance and angle ratio and this completes our session. Hope you all have enjoyed the session.