Question

Cho hình chóp \(S.ABC\) có \(SA \bot SB,SB \bot SC,SC \bot SA\). Chứng minh rằng:

a) \(\left( {SAB} \right) \bot \left( {SBC} \right)\);

b) \(\left( {SBC} \right) \bot \left( {SCA} \right)\);

c) \(\left( {SCA} \right) \bot \left( {SAB} \right)\).

Answer 1

a) Ta có:

\(\left. \begin{array}{l}\left. \begin{array}{l}SA \bot SB\\SA \bot SC\end{array} \right\} \Rightarrow SA \bot \left( {SBC} \right)\\SA \subset \left( {SAB} \right)\end{array} \right\} \Rightarrow \left( {SAB} \right) \bot \left( {SBC} \right)\)

b) Ta có:

\(\left. \begin{array}{l}\left. \begin{array}{l}SA \bot SB\\SA \bot SC\end{array} \right\} \Rightarrow SA \bot \left( {SBC} \right)\\SA \subset \left( {SCA} \right)\end{array} \right\} \Rightarrow \left( {SCA} \right) \bot \left( {SBC} \right)\)

c) Ta có:

\(\left. \begin{array}{l}\left. \begin{array}{l}SA \bot SB\\SB \bot SC\end{array} \right\} \Rightarrow SB \bot \left( {SCA} \right)\\SB \subset \left( {SAB} \right)\end{array} \right\} \Rightarrow \left( {SAB} \right) \bot \left( {SCA} \right)\)