∴AA 1∥DD 1，ab∑CD...( 1)
∵DD 1、CD？ Plane CDD 1C 1, AA 1, AB? Plane CDD 1C 1,
∴AA 1∥ plane CDD 1C 1, ab∑ plane CDD 1C 1, …(3 points)
∵AA 1、AB？ Plane AA 1B 1B, and AA 1∩AB=A,
∴ plane aa 1b 1b∑ plane CDD 1C 1, …(4 points)
∫af∑EC 1, ∴A, E, C 1 and F coplanar ... (5 points)
∫ Plane AEC 1F∩ Plane AA 1B 1B=AE, Plane AEC 1F∩ Plane CDD1= FC/kloc-0.
∴ae∥fc 1； ... (7 points)
(2) Let AC and BD connect at point O, AC 1 and EF connect at point O 1, and connect at point O1.
∵ quadrilateral ABCD, quadrilateral AEC 1F are parallelograms,
∴O is the midpoint of AC and BD, O 1 is the midpoint of AC 1 and EF ... (8 points)
∵be∥df,∴o 1o= 12c 1c= 12(be+ef).
∫be = 1, DF=2, ∴ CC 1 = 3...( 10)
∵AA 1⊥ plane ABCD, quadrilateral AEC 1F is a square,
∴△ACC 1, △ABE and △ADF are right triangles, so.
AC2 = AC 12-cc 12 = 2ae 2-cc 12 = 12-9 = 3，AB2=AE2-BE2=6- 1=5
BC2=AD2=AD2-DF2=6-4=2
∴AC2+BC2=5=AB2, you can get AC ⊥ BC ... (12 points).
∵BB 1⊥ aircraft ABCD, AC? Plane ABCD
∴AC⊥BB 1.
∵BC and BB 1 are straight lines intersecting in the plane bb1c1c.
∴AC⊥ aircraft BB 1C 1C? ... (13)
∵EC 1？ Plane BB 1C 1C
∴ AC ⊥ EC 1...( 14 points)