(1) is correct; A'CDF is a square, which means that A'F is just the center line of ABCD, so: AF=BA'= 1.

Point e and point b coincide, EF is the diagonal of square ABA 'f, and EF=√2.

(2) error; EF can be translated on the boundary, and there are many situations, so it is not right.

(3)EF=√5, which can only coincide with the diagonal BD=√5 of ABCD. BA'CD is an isosceles trapezoid.

(4)BA'CD is an isosceles trapezoid, which can only be BA'=CD, and EF coincides with BD, so EF=√5.

The correct one is ① ③ ④.