(1) As shown in Figure 1, isosceles △ ABC and isosceles △ Dec have a common point C, and ∠ BCA = ∠ ECD, connect be and ad, if BC = AC, EC = DC, prove: be = ad. (2) if △ Dec is rotated around point C to figure 2, figure 3 and figure 4, other conditions remain unchanged, are be and ad still equal? Why?

It is proved that: (1) in △ BCE and △ ACD, BC = AC ∠ BCE = ∠ acdec = CD, ≌ BCE ≌ ACD (SAS), and ≌ be = ad. (2) in Fig. 2, Fig. 3 and Fig. 4, be and AD are equal. The reason is as follows: as shown in Fig. 2, Fig. 3 and Fig. 4, ≌ BCA = ECD, ≌ ACD + BCA = 180 degree, ≌ ECD + BCE = 180 degree, ≌ BCE = 180 degree In △ BCE and △ ACD, BC = AC ∠ BCE = ∠ acdce = CD, ≌ BCE ≌ ACD (SAS), ≌ be = ad

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