如图所示\( ,​\)在直三棱柱\( ABC-{A}_{1}{B}_{1}{C}_{1}​\)中\( ,​\)已知AC
\( \text{⊥BC},BC={C}_{1}C,\mathrm{设}A{B}_{1}​\)的中点为\( D,{B}_{1}C{\text{∩BC}}_{1}​\)=E.

求证:(1)DE//平面\( A{A}_{1}{C}_{1}C;​\)
(2)\( B{C}_{1}{\text{⊥AB}}_{1}.​\)