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用代数法(在高二课程中叫做解析法)证明几何题,是把几何图形移放在直角坐标系内,把对几何图形的研究化为对代数方程来研究。这种方法对于扩大证明几何问题的思路起着积极的作用,它还能进一步巩固刚刚学完的点的坐标、两点间的距离、定比分点、中点坐标、直线方程、曲线交点和曲线的切线等解析几何的基础知识,因此我们加强了这一课题的教学。下面谈谈我们的体会。一、坐标系的选取是解题的重要一环。把几何图形移入坐标系内,其每个顶点位置的确定,需要有两个坐标,为了使解题尽可能简单些,就必须选取适当的坐标系。
The use of algebraic methods (called analytic methods in the second year of the course) to prove geometric problems is to move the geometry into a rectangular coordinate system and study the geometry as an algebraic equation. This method plays an active role in expanding the ideas for proving geometric problems. It can further consolidate the coordinates of the points that have just been learned, the distance between two points, the point of the fixed point, the coordinates of the midpoint, the equation of the line, the point of intersection and the curve The basic knowledge of tangent and other analytical geometry, so we have strengthened the teaching of this subject. Let’s talk about our experience. First, the choice of coordinate system is an important part of problem solving. To move the geometry into the coordinate system, the position of each vertex must have two coordinates. To make the solution as simple as possible, you must select the appropriate coordinate system.