Question

Paralelipipedul dreptunghic abcda'b'c'd' are ab=9 cm, AA' = 3 radical 3 cm si AD = 3 cm.

a. aratati ca A'B perpendicular BC
b. determinati m((A'BC),(ABC));
c. aratati ca A'D perpendicular DC
d. determinati m((A'B'C),(ABC)).

Answer 1

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°