AB is a line segment and P is its midpoint. D and E are Points on the same side of AB such that Angle BAD = Angle ABE and Angle EPA = Angle DPB show that - Triangle DAP is congruent to Triangle EBP................is my answer to this correct?
Dear Student
It is given that ∠EPA = ∠DPB
⇒ ∠EPA + ∠DPE = ∠DPB + ∠DPE
⇒ ∠DPA = ∠EPB
In 
DAP and EBP,
∠DAP = ∠EBP (Given)
AP = BP (P is mid-point of AB)
∠DPA = ∠EPB (From above)
∴ ΔDAP ≅ ΔEBP (ASA congruence rule)
∴ AD = BE (By CPCT)
Regards