13 面面平行的判断与性质

例题

解：

$\because C_1{D}_1\parallel =AB$

$\therefore AB{C}_1{D}_1$ 是平行四边形

$\therefore A{D}_1\parallel B{C}_1$ ，又 $B{C}_1\subset \mathrm{面}BD{C}_1$，$A{D}_1\not\subset BD{C}_1$

$\therefore A{D}_1\parallel \mathrm{面}BD{C}_1$

同理 $A{B}_1\parallel \mathrm{面}BD{C}_1$，

$A{B}_1,A{D}_1\subset \mathrm{面}A{B}_1{D}_1$

且 $A{B}_1\bigcap A{D}_1=A$

$\therefore A{B}_1\bigcap A{D}_1=A$

$\therefore \mathrm{面}A{B}_1{D}_1\parallel \mathrm{面}{C}_{1}BD$