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立体几何研究的对象位于三度空间,它是从平面几何发展而来的。因此二者之间存在着密切的联系。 一般地讲,在平面几何中图形直观,便于启发学生思考。而在立体几何中,不易树立空间观念,遇到实际问题,学生往往不会画图,即使画出图形也不能清楚地了解图形结构,给解题带来了很大的困难。如果我们能经常注意到立体几何与平面几何的联系,在教学和辅导中有意识地引导学生将立体几何问题转化为类似的平面几何问题,先从类似的平面几何问题入手,找出解题的方法,那么对于培养和提高学生立体几何解题能力是很有帮助的。以下举例说明。
The object of the three-dimensional geometry study is located in the third dimension, which is derived from the plane geometry. Therefore, there is a close connection between the two. In general, the graphic is intuitive in plane geometry and it is easy to inspire students to think. In the three-dimensional geometry, it is not easy to establish the concept of space and encounter practical problems. Students often do not draw pictures. Even if the figures are drawn, they cannot clearly understand the structure of the figures, which brings great difficulties to the problem solving. If we can always pay attention to the connection between the three-dimensional geometry and the plane geometry, consciously guide students in the teaching and coaching to transform the three-dimensional geometry problem into a similar plane geometry problem, start with similar plane geometry problems, and find out the solution to the problem. , it is very helpful for cultivating and improving students’ ability to solve problems in three-dimensional geometry. The following is an example.