設(shè)
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為互不重合的平面,
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為互不重合的直線,給出下列四個(gè)命題:
①若
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; ②若
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∥
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∥
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,則
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∥
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;
③若
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; ④若
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.
其中正確命題的序號為
分析:①線面垂直,則線垂直于該平面內(nèi)任一條線;②只有一平面內(nèi)兩相交直線都與另一平面平行,這兩平面才平行;
③面面垂直,則一平面內(nèi)垂直于交線的直線必垂直于另一平面;④要特別注意直線在平面內(nèi)這種情況.
解答:解:①由線面垂直的性質(zhì)可得;②若m∥n,則結(jié)論錯(cuò)誤;③由面面垂直的性質(zhì)可得;④n還可能在β內(nèi),則結(jié)論錯(cuò)誤.
故正確答案為①③.
點(diǎn)評:本題考查線線、線面、面面的平行和垂直關(guān)系;同時(shí)考查空間想象能力.
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