 Hello friends, let's discuss the following question. It says A, B, C, D is a quadrilateral in which A, D is equal to B, C and angle B, A, B is equal to angle C, B, A. Prove that triangle A, B, D is congruent to triangle B, A, C and B, D is equal to A, C and angle A, B, D is equal to angle B, A, C. To prove this we will be using SAS congruence criteria. Let us now understand what is SAS congruence criteria. If we have two triangles say A, B, C, D, E, F then one triangle is congruent to other triangle by SAS congruence criteria if two sides and one included angle of one triangle is equal to two sides and one included angle of other triangle. So this knowledge will work as a idea. Let us now proceed on with the solution. Now in triangle A, B, D and B, A, C we are given that A, D is equal to B, C and we are given that angle D, A, B is equal to angle C, B, A. Now we see that in triangles A, B, D and B, A, C A, B is common. So A, B is equal to A, B since is the common side. So we have proved that two sides and one included angle of triangle A, B, D is equal to two sides and one included angle of triangle B, A, C. Therefore triangle A, B, D is congruent to triangle B, A, C by SAS congruence criteria. Now in the second part we have to prove B, D is equal to A, C. Now since triangle A, B, D is congruent to triangle B, A, C therefore by CPCTC B, D is equal to A, C. As we know that corresponding parts of congruent triangles are congruent therefore we have B, D is equal to A. Now in the third part we have to prove angle A, B, D is equal to angle B, A, C. Now again since triangle A, B, D is congruent to triangle B, A, C therefore by CPCTC angle A, B, D is equal to angle B, A, C. As we know that corresponding parts of congruent triangles are congruent. Hence we have proved that triangle A, B, D is congruent to triangle B, A, C, B, D is equal to A, C and angle A, B, D is equal to angle B, A, C. So this completes the question. Hope you enjoyed the session. Goodbye and take care.