The nature of rotation; Congruent triangles's judgment; The nature of isosceles triangle; Properties of parallelogram; Determination of rectangle.

(1) According to AB=BC, it can be proved that ∠CAB=∠ACB, then in △ABC and △AEP, there are two angles corresponding to each other, which can be proved according to the theorem of triangle internal angle sum;

(2) If ∠EPA=∠EAP is known from (1), then AC=DP, which can be proved by the fact that parallelograms with equal diagonals are rectangles;

(3) It can be proved that △ EAM △ EPN, so that EM = en can be obtained.

(1) proves that in △ABC and △AEP,

∠∠ABC =∠AEP，∠BAC=∠EAP，

∴∠ACB=∠APE，

In △ABC, AB=BC,

∴∠ACB=∠BAC，

∴∠EPA=∠EAP.

(2) Solution:? APCD is rectangular. The reason for this is the following：

∵ Quadrilateral APCD is a parallelogram,

∴AC=2EA,PD=2EP，

∫from( 1)≈EPA =∠EAP，

∴EA=EP，

AC=PD，

∴? APCD is rectangular.