线面平行,几何术语。定义为一条直线与一个平面无公共点(不相交),称为直线与平面平行。平面外一条直线与此平面内的一条直线平行,则该直线与此平面平行。平面外一条直线与此平面的垂线垂直,则这条直线与此平面平行。
线面平行判断方法
(1)利用定义:证明直线与平面无公共点;
(2)利用判定定理:从直线与直线平行得到直线与平面平行;
(3)利用面面平行的性质:两个平面平行,则一个平面内的直线必平行于另一个平面。
注:线面平行通常采用构造平行四边形来求证。
证明线面平行的方法
一,面外一条线与面内一条线平行,或两面有交线强调面外与面内版
二,面外一直线上不同两点到面的权距离相等,强调面外
三,证明线面无交点
四,反证法(线与面相交,再推翻)
五,空间向量法,证明线一平行向量与面内一向量(x1x2-y1y2=0)
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