 Hi and welcome to the session. Let's discuss the following question. It says in quadrilateral AC BD, AC is equal to AD and AB bisects angle A. Show that triangle ABC is congruent to triangle ABD. What can you say about BC and BD? So the key idea behind this question is, we will be using SAS congruence criteria. So this is the key idea. Now SAS congruence criteria means two sides and included angle of one triangle is equal to the two sides and one included angle of the other triangle. So let's move on to the solution now. We are given AC is equal to AD and AB bisects angle A and we have to prove triangle ABC is congruent to triangle ABD. Let's now start the proof. Now in triangle ABC and triangle ABB, AC is equal to AD. It is given to us and angle BAC is equal to angle BAD because we are given that AB bisects angle A. Also AB is equal to AB because it's the common side. Now since we have shown that two sides and the included angle of two triangles are equal therefore triangle ABC is congruent to triangle ABD by SAS congruence criteria. Now since two triangles are congruent therefore BC is equal to BD by CPCTC that is corresponding paths of congruent triangles are congruent. Hence the result is proved that is two triangles are congruent and for the second part answer is BC is equal to BD that is they are equal. So this completes the question. Bye for now. Take care. Hope you enjoyed the session.