 Hello and welcome to the session. In this session we will discuss effects of rigid motion on a given figure after transformation and we will see if the two figures are congruent or not. Now we have learnt that figures in a plane can be reflected, rotated or translated to produce new figures. Now in our earlier sessions we had discussed about rigid transformations and isometry and now let us recall rigid transformations. Now rigid transformations are those transformations that do not change the shape and size of a figure. That is they preserve the distance between the points and angle measure. Now transformation, reflection and rotation are rigid transformations and these transformations are called rigid motions. And now let us discuss effect of rigid motion on a given figure. Now here let us take an example of rotation. Suppose I have a cardboard cut in a shape of triangle. Let its vertices be P, Q and R. Now if this triangle PQR is rotated about a fixed point by a certain angle we obtain its rotated image as triangle P dash Q dash R dash. Since we do not view any alteration in its angles and length of its sides while rotating so corresponding angles. The two triangles are equal. We have of line segment PR is equal to distance of line segment P dash R dash of line segment QR is equal to distance of line segment Q dash R dash. Line segment PQ is equal to distance of line segment P dash Q dash. Also measure of angle RQP is equal to measure of angle R dash Q dash P dash. Measure of angle PRQ is equal to measure of angle P dash R dash Q dash and measure of is equal to measure of angle Q dash P dash R dash. This is preserved. Also preserved is a rigid motion is a rigid motion and reflection are rigid motions. And now let us discuss congruence. Two figures are congruent exactly the same shape and if one figure is cut out and it can be placed exactly on the top of other then these figures are congruent. Now see the following figures we replaced on the other figure. Blue star exactly lie above the orange star over the blue star. It will also exactly lie over the blue star. Thus the two stars that this green circle will be smaller than this blue circle exactly on the blue circle. So here the two, whether the two figures are congruent when rigid motions like translation, rotation and reflection are performed on the figure. The triangle PQ are about a fixed point by a certain angle and we are getting its rotated image as triangle P dash Q dash R dash. Now let us place R dash over triangle PQ on the pre-image point P dash what is Q over Q dash and R dash and here we observe that triangle P dash Q dash R dash lies exactly where PR is equal to line segment P dash R dash. Then line segment Q is equal to line segment Q dash R dash and line segment PQ is equal to line segment P dash Q dash. q dash is equal to measure of angle r dash q dash p dash. r q is equal to measure of angle p dash r dash q dash to measure of angle r dash p dash q dash. Thus, we observe one rigid motion like translation, rotation and reflection are performed on a geometrical figure. Then the two figures, that is the pre-image and congruent. We also conclude that two congruents, if their correspondence, you must note that dilation rigid motion requires it increases or decreases the size of figure after dilation is not called a figure. Hope you all have enjoyed the session.