In the rectangular ABCD, there are AB = CD, ∠ B = ∠ C = 90.

∠PDC = 45°，∠c = 90°，,∴∠DPC =∠PDC = 45°

∴DC=PC=AB

∫∠APD = 90，∠APD+ ∠APB+ ∠EPC= 180

∴ ∠APB+∠EPC=90

∠∠BAP+∠APB = 90

∴ ∠BAP= ∠EPC

∴△BAP≌△CPE(ASA)

∴AP=EP