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一、借助三角形中位线找平行线三角形的中位线平行于第三边.在平面几何解题时经常会由中点联想到中位线,在立体几何中同样需要这样思考.例1 P是平行四边形ABCD所在平面外的一点,Q是PA的中点,求证:PC∥平面BDQ.分析要证PC∥平面BDQ,只要在平面BDQ内找到一条直线与PC平行即可.又Q是PA的中点,故可联想中位线寻找平行线.
First, with the triangular median line to find the parallel line Triangle of the median line parallel to the third side in the plane geometry problems often think of the median line from the mid-point, in the three-dimensional geometry also need to think so.Example 1 P Is a point outside the plane where the ABCD quadrilateral, Q is the midpoint of the PA, verify: PC∥ plane BDQ. Analysis to prove PC∥ plane BDQ, as long as the plane BDQ to find a straight line and the PC can be parallel. Q is PA The midpoint, so you can think of the median line to find parallel lines.