Analysis: (1), AB=CD, AD=BC from the nature of parallelogram, BC = BC' ′, CE = C ′ E from the nature of folding.

(2) In Figure A, BC=AD, BC∨C' d, and in Figures A and B, we know △ ABC '△ DCF? AC'=DF？ AC'+C'D=C'D+DF？ AD=C'F', that is, BC = c' F. It is easy to prove that quadrilateral BCFC' is a parallelogram, BC=BC' is a rhombus composed of a group of parallelograms with equal sides, and quadrilateral BCFC' is a rhombus.

Answer:

Solution:

(1) Write any four pairs of equal line segments in AB=CD, AD=BC, BC=BC', EC=EC', BC'=AD;

(2) Proof 1: In Figure A,

∫ quadrilateral ABCD is parallelogram BC=AD, BC∨C' d.

In Figure A and Figure B, we know △ ABC '△ DCF, ∴AC'=DF according to the meaning of the question.

∴AC'+C'D=C'D+DF

∴AD=C'F'

That's BC = c 'f

Once again, BC, C 'f

∴ Quadrilateral bcfc' is a parallelogram,

From the nature of folding, BC = BC'

∴ quadrilateral BCFC' is a diamond.