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中学几何中有许多命题涉及到求定值问题,其中最常见的有:求证按某种规律变动的线段的和、差、积、比,夹角与图形面积的定值,求证某种变动直线有定向和过定点等。南于定值问题条件稳蔽,要有较强的分析判断能力才能找出其定值,加之习题类型较多,平时练习又较少,所以学生往往感到困难。笔者在高二数学总复习中,根据求证定值问题的命题特征,采用如下两种求解方法:一种是通过变动条件在“特殊位置”上显示出的特征,找出定值是什么值,使问题转化为学生熟知的证明题。另一种是对于不易求出定值是什么值的命题,首先找出题设的固定部份和变动部份,然后分析和观察固定部份和变动部份之间的联系,从变中寻找出不变的因素,由不变因素找出证题途径。现就这两种方法分别举例说明。
There are many propositions in the geometry of middle schools involving the determination of fixed values. The most common ones are: verifying the sum, difference, product, ratio of line segments that change according to a certain rule, setting values of the included angles and the area of the figure, and verifying the line of certain changes. There are orientations and over-fixed points. The problem of stability in the South in the fixed-value problem requires a strong ability of analysis and judgment to find out its fixed value. In addition, there are many types of exercises and there are few exercises at ordinary times, so students often feel difficult. During the second year of mathematics review, the author used the following two methods to solve the propositional features of the verification value question: One is to find out what the value of the fixed value is by displaying the characteristics of the change condition in the “special position”. The question turns into a student’s well-known proof. The other is for the proposition that it is not easy to find out what the fixed value is. First, find out the fixed part and the change part of the question, then analyze and observe the connection between the fixed part and the changing part, and look for the change from the change. Invariable factors, from the invariable factors to find out the testimony approach. The two methods are illustrated separately.