a) BC⊥(ABB'A')pt ca ABCDA'B'C'D' paralelipiped dreptunghic, BC⊥(ABB'C'C)
sau CB⊥AB, pt ca ABCD dreptunghi
CB⊥B'B pt ca CBB'C' dreptunghi
deci BC⊥A'B⊂(A'ABB')
b) (A'BC) ≡(A'BCB')
(A'BC)∩(ABC)=BC
BC⊥AB, AB⊥BC
BC⊥A'B, A'B⊥BC
⇒m∡((A'BC), (ABC))=m∡(A'B,Ab)=m∡A'BA
tg∡A'BA=3√3/9=√3/3⇒m∡∡A'BA=30°
c)DC⊥(ADD'A')⇒DC⊥A'D⊂(ADD'A')
(A'B'C)≡(A'B'CD)
(ABC)≡(ABCD)
(A'B'C∩(ABC)=CD
din considerente teoretice analoge cuceklede la puncteler a) si b)
, m∡((A'B'C) , (ABC))=m∡(B'c, Bc)=m∡B'CB
tg∡B'CB=B'B/BC=3√3/3=√3⇒m∡B'CB=60°
