試題分析:當(dāng)點(diǎn)
為
的中點(diǎn)時(shí),由對稱性可知
也是
的中點(diǎn),此時(shí)
//
,因?yàn)?img src="http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824033604397877.png" style="vertical-align:middle;" />,
,所以
//
,故A正確;
假設(shè)
,因?yàn)?img src="http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824033604507721.png" style="vertical-align:middle;" />,所以
。所以四邊形
為菱形或正方形,即
。因?yàn)?img src="http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824033603961765.png" style="vertical-align:middle;" />為正方體所以
。所以假設(shè)不成立。故B不正確。
因?yàn)?img src="http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824033604616608.png" style="vertical-align:middle;" />為正方形,所以
,因?yàn)?img src="http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824033604647761.png" style="vertical-align:middle;" />,
,所以
,因?yàn)?img src="http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824033604709631.png" style="vertical-align:middle;" />,所以
。因?yàn)?img src="http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824033604741642.png" style="vertical-align:middle;" />,所以
。同理可證
,因?yàn)?img src="http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824033604803700.png" style="vertical-align:middle;" />,所以
,因?yàn)?img src="http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824033604850597.png" style="vertical-align:middle;" />,所以
。故C正確。
設(shè)正方體邊長為
,則
。故D正確。