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)


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