Question

In cubul ABCDA'B'C'D' demonstrează ca : a) BD_|_ (ACA') b) BD'_|_(AB'C)

Answer 1

a)

[tex]\it A'A\perp(ABD), \ \ BD \subset (ABD) \Longrightarrow A'A\perp BD \Longrightarrow BD\perp A'A \ \ \ (1) \\\;\\ BD \perp AC (diagonalele\ p\breve{a}tratului) \ \ \ \ (2) \\\;\\ A'A \cap AC = \{A\} \ \ \ \ (3) [/tex]

$\it (1), (2), (3) \Longrightarrow BD \perp (ACA')$