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【题目】已知a,b表示直线,α,β,γ表示平面,则下列推理正确的是

A.α∩β=a,bαab

B.α∩β=a,a∥bb∥α且b∥β

C.a∥β,b∥β,aα,bαα∥β

D.α∥β,α∩γ=a,β∩γ=ba∥b

答案D

解析选项A中,α∩β=a,bα,则a,b可能平行也可能相交,故A不正确;

选项B中,α∩β=a,a∥b,则可能b∥α且b∥β,也可能b在平面α或β内,故B不正确;

选项C中,a∥β,b∥β,aα,bα,根据面面平行的判定定理,再加上条件a∩b=A,才能得出α∥β,故C不正确;

选项D为面面平行性质定理的符号语言,故选D.

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