 Hello and welcome to the session. I am Asha and I am going to help you with the following question which says, in triangle ABC and triangle DEF, AB is equal to DE, AB is parallel to DE, BC is equal to EF and BC is parallel to EF. Vertices A, B and C are drawn to vertices DEF respectively. We have to show the following six parts. So here we are given that in triangle ABC and triangle DEF, AB is equal to DE, AB is parallel to DE, BC is equal to EF and BC is parallel to EF. And vertices AB and C are joined to vertices DE and F respectively. And first we have to prove is that, coordinate A, B, ED is a parallelogram. Let us now start with the proof. Now in the quadrilateral, ED, AB is equal to ED, AB is parallel to ED. These are given to us. Therefore, quadrilateral, BED is a parallelogram. A quadrilateral is a parallelogram to parallel. And here in this figure, AB is equal to DE and AB is parallel to DE also. So this is the pair in this quadrilateral which is equal in parallel also. Therefore, it is a parallelogram. So this completes the first part. And now proceeding on to the second part, where we have to prove that quadrilateral, BEFC is a parallelogram. Now again here, BC is equal to EF and also BC is parallel to EF. So this implies BEFC is a parallelogram. Against this in the quadrilateral, if a pair of opposite sides are equal in parallel then it is a parallelogram. Therefore, this is also a parallelogram. So this completes the second part. On to the third part, where we have to prove AD is parallel to CF, AD is equal to CF. Now since BEED is a parallelogram by part one, this implies AD is equal to DE. AD is parallel to BE in a parallelogram. Both the pairs of pull and parallel is a parallelogram. This implies that BE is equal to CF, BE is parallel to CF since in a parallelogram both the pairs of opposite sides are equal and parallel. From these two, we can say that AD is equal to CF and AD is parallel to CF. Since they are equal to the same line, then they are equal to each other and if two lines are parallel to the same line, they are parallel to each other. So this proves the third part. And now proceeding on to the fourth part, where we have to prove that quadrilateral AFD is a parallelogram. Now in this quadrilateral we have AD is equal to CF, AD parallel to CF since by part three. So this implies quadrilateral DFD is a parallelogram. Since in a quadrilateral if a pair of opposite sides are equal and parallel, then it is a parallelogram. So this completes the fourth part and now proceeding on to the fifth part that AC is equal to DF. Now since in part four, we have proved that ACFD is a parallelogram. So this implies that AC is equal to FD since opposite sides of a parallelogram are equal. So this completes the fifth part and now proceeding on to the last part which is to prove that triangle ABC is congruent to triangle DEF. Now in these two triangles AB is equal to DE this is given BC is equal to EF this is also given AC is equal to FD this we have proved in part five. So by SSS congruence condition we can say that triangle ABC is congruent to triangle DEF. So this completes the session take care and bye for now.