Verified answer

1)

AB║A₁B₁║D₁C₁║DC; AD ║BC ║B₁C₁║A₁D₁; AA₁║BB₁║CC₁║DD₁

2)

AA₁ ⊥ AB,A₁B₁ ,A₁D₁ ,AD

BB₁ ⊥ BA,B₁A₁ ,B₁C₁ ,BC

CC₁ ⊥ CB,C₁B₁ ,C₁D₁ ,CD

DD₁ ⊥ DA,D₁A₁ ,D₁C₁ ,DC

3)

AA₁ /· BC,B₁C₁ ,D₁C₁ ,DC

BB₁ /· AD,A₁D₁ ,C₁D₁ ,CD

CC₁ /· BA,B₁A₁ ,D₁A₁ ,DA

DD₁ /· AB,A₁B₁ ,C₁B₁ ,CB

4)

(ABC)║(A₁B₁C₁ ); (ABB₁ )║(DCC₁ ); (BCC₁ )║(ADD₁ )

5)

(ABB₁ ) ⊥ (ABC),(BB₁C₁ ),(B₁A₁D₁ ),(A₁AD)

(DCC₁ ) ⊥ (DCB),(CC₁B₁ ),(C₁D₁A₁ ),(D₁DA)

(BCC₁ ) ⊥ (BCD),(B₁C₁D₁ )

(ADD₁ ) ⊥ (ADC),(A₁D₁C₁ )