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在立体几何教学中,必须重视培养学生把立体问题转化为平面问题的能力。这是因为在立体几何中不少问题是规定或归结为平面问题来解释或解决的,如直线与平面的夹角定义为直线与它在此平面内的射影的夹角,平面与平面的夹角的度量定义为它的平面角的度量;异面直线的距离归结为平面上点到直线的距离;线面平行的判定归结为线线平行的判定等等。在解决一些空间问题时,也需要通过各种途径转化为平面问题。这种转化规律的研究,也成为立体几何教学研究中的重要一环。
In the three-dimensional geometry teaching, we must pay attention to the ability of students to transform the three-dimensional problem into a plane problem. This is because many problems in the three-dimensional geometry are clarified or attributed to planar problems to explain or solve, such as the angle between the straight line and the plane is defined as the angle between the straight line and its projection in this plane, and the plane and plane clamps. The measure of the angle is defined as the measure of its planar angle; the distance of the straight line of the opposite surface is reduced to the distance from the point to the straight line in the plane; the determination of the parallel line surface is attributed to the determination of the line parallelism and so on. In solving some space problems, it also needs to be transformed into planar problems through various channels. This study of transformation laws has also become an important part of the study of solid geometry teaching.