问题 选择题

已知A、B是两个不同的点,m、n是两条不重合的直线,α、β是两个不重合的平面,则①m⊂α,A∈m⇒A∈α;②m∩n=A,A∈α,B∈m⇒B∈α;③m⊂α,n⊂β,mn⇒αβ;④m⊂α,m⊥β⇒α⊥β.其中真命题为(  )

A.①③

B.①④

C.②③

D.②④

答案

对于①,根据平面的基本性质,可得结论A∈α,故①正确;

对于②,点B可能在α内,也可能在平面α外,故②不正确;

对于③,根据面面平行的判定定理,不能得出αβ,故③不正确;

对于④,m⊂α,m⊥β,则利用面面平行的判定,可得α⊥β.④正确.

其中真命题为①④.

故选B.

单项选择题
填空题


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