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在一定条件下,空间图形可以通过平面旋转、表面展开等方法转变为平面图形,在转化过程中,空间图形的元素间的数量关系或位置关系,有的发生变化;有的没有发生变化。利用“展平法”可以寻求证题路线,简化证题过程。搞清转化中的变量和不变量是解这类问题的关键。例1 在空间四边形ABCD中,AB=AD,CB=CD,求证:AC⊥BD。分析把平面ABD绕BD旋转,使它和平面BCD重合,这时ABCD就转变为平面四边形,因为仍有AB=AD,CB=CD,故AC是BD
Under certain conditions, the spatial pattern can be transformed into a planar pattern by means of plane rotation, surface unfolding, etc. In the process of transformation, the quantity relationship or positional relationship between the elements of the spatial pattern changes, and some changes do not occur. Using the “flattening method” can seek the testimony route and simplify the process of the testimony. Finding out the variables and invariants in transformation is the key to solving such problems. Example 1 In the space quadrilateral ABCD, AB=AD, CB=CD, verification: AC⊥BD. The analysis rotates the plane ABD around the BD so that it coincides with the plane BCD. At this time, the ABCD is transformed into a planar quadrilateral. Since there are still AB=AD, CB=CD, AC is a BD.