Cho tứ diện ABCD có AB vuông góc ( BCD) . Trong \(\Delta BCD\) vẽ các đường cao

a) Đúng

b) Đúng

c) Sai

d) Đúng

 

Ta có \[\left. \begin{array}{l}CD \bot BE\\CD \bot AB\end{array} \right\} \Rightarrow \left. \begin{array}{l}CD \bot \left( {ABE} \right)\\CD \subset \left( {ADC} \right)\end{array} \right\} \Rightarrow \left( {ADC} \right) \bot \left( {ABE} \right)\].

Vậy a đúng.

\[\left. \begin{array}{l}DF \bot BC\\DF \bot AB\end{array} \right\} \Rightarrow \left. \begin{array}{l}DF \bot \left( {ABC} \right)\\AC \subset \left( {ABC} \right)\end{array} \right\} \Rightarrow \left. \begin{array}{l}DF \bot AC\\DK \bot AC\end{array} \right\} \Rightarrow \left. \begin{array}{l}AC \bot \left( {DFK} \right)\\AC \subset \left( {ADC} \right)\end{array} \right\} \Rightarrow \left( {ADC} \right) \bot \left( {DFK} \right)\]

Vậy b đúng.

Ta có \[\left. \begin{array}{l}CD \bot BE\\CD \bot AB\end{array} \right\} \Rightarrow \left. \begin{array}{l}CD \bot \left( {ABE} \right)\\CD \subset \left( {BDC} \right)\end{array} \right\} \Rightarrow \left( {BDC} \right) \bot \left( {ABE} \right)\].

Vậy d đúng.