 Hello and welcome to the session. In this session, we will use definition of congruence in terms of rigid motions to show that two triangles are congruent if and only if corresponding sides and corresponding angles of these two triangles are equal. Now we know two triangles are said to be congruent if one can be exactly superimposed on the other by a rigid motion that is transformation of points in space consisting of one or more translations, reflections and rotations because rigid motions preserve the distance and angle measure. Now let us discuss corresponding paths of congruent triangles. Now triangles that are of same size and shape are paired congruent triangles. Now each triangle has six corresponding paths are congruent then triangles are congruent or we can say if all the six corresponding paths are equal then triangles are congruent. Now let us consider two triangles that is triangle ABC and triangle EFG. Now let triangle EFG is translated image of triangle ABC translation preserves distance and angle measure therefore triangle EFG can be superimposed on triangle ABC. Now we know that are said to be congruent if one can be exactly superimposed on the other by a rigid motion. So here as triangle EFG can be superimposed on triangle ABC thus triangle is congruent to triangle EFG. Now first of all we find the corresponding vertices of the two triangles. Now here you can see vertex B is translated to vertex F, B corresponds to F, vertex A is translated to vertex E to E also vertex C is translated to vertex G so to G that the vertices of the two triangles correspond in the same order as the letters naming the triangles ABC is congruent to triangle EFG and here A corresponds to E, B corresponds to F corresponds to G. Now the corresponding vertices can be used to name corresponding of the two triangles we have angle B whose corresponding angle is angle F and we have angle C the shape is same because they can be superimposed on each of them that is these two triangles will be equal angle E, angle B is equal to angle F and angle C is equal to angle G. Similarly FAB is side EF corresponding side of BC is side actually. Now since the difference must be same with EF that is line segment AB is equal to line segment EF similar. Two triangles are congruent then the angles are equal. Similarly if the corresponding equal then the two triangles are congruent. Two triangles are congruent if and only if they are correspond equal. Now notice this is an example here now from this figure we have two triangles triangle and triangle DFB and where we see in triangle A angle DFB is equal to angle D it is given here to angle B 8AF of triangle AFC and side DF of triangle DFB are equal. Line segment AF is equal to line segment DF. Here also you can see line segment CF is equal to line segment DF. Line segment is equal to line segment DB equal to angle DFB of these two triangles are equal triangles that is triangle into triangle DFB. So in this session we have learnt that two triangles are congruent if the corresponding parts are equal and this completes our session hope you all have enjoyed the session.