 Hi, and welcome to the session. Let's discuss the following question. It says a b is a line segment and P is its midpoint D and E are points on the same side of AB such that angle BAD is equal to angle ABE and angle EPA is equal to angle DPB. Show that triangle DAP is congruent to triangle EPB and ADA is equal to BE. So to prove two triangles are congruent we'll be using ASA congruence criteria. By which we need to show that two angles and included side of the two triangles are equal. So this is the key idea. Now we are given that P is midpoint of AB. That is AP is equal to BP and we are also given that angle BAD is equal to angle AB E and angle EPA is equal to angle DPB and we have to prove that triangle DAP is congruent to triangle EBP and we also have to show that AD is equal to BE. Let's now move on to the solution. We are given that angle EPA is equal to angle DPB which implies that angle EPA plus angle EPD is equal to angle DPB plus angle EPD. So this implies angle APD is equal to angle BPE because angle EPA plus angle EPD is equal to angle APD and angle DPB plus angle EPD is equal to angle BPE. Now in triangles DAP and EBP we have angle DAP is equal to angle EBP this is given to us and AP is equal to BPE because P is the midpoint of AB. We have proved that angle APD is equal to angle BPE. So we have proved that two angles and one included side of the two triangles are equal therefore triangle DAP is congruent to triangle EBP by ASA criteria. Now since two triangles are congruent their corresponding parts are also congruent therefore AD is equal to BPE by CPCTC that is corresponding parts of congruent triangles are congruent. Hence we have proved that triangle DAP is congruent to triangle EBP. We have also proved that AD is equal to BPE. So this completes the question. Bye for now. Take care. Hope you enjoyed the session.