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有些平面几何題目,把它們的条件或結论等加以变更后,可以得出新的结论来。我們在几何教学中如果有意识地、经常地指导学生从这方面进行思考、这对培养他們的邏輯论证和独立工作的能力,很有好处。下面就介紹几种做法。一、改变題中的数字为字母,推出一股规律。有些几何題是论证或推算田形之間的数值关系的,若把数字換作字母,解出以后便能找出这一类題目变化的一般规律和图形中的新的关系。这样,就可以把对个别的、特殊的图形的研究,換作对同类型題的一般性的研究。例如有这样一个題目:“作一矩形和巳知正方形等积,并且使矩形的周长等于已知正方形周长的1 1/4倍。”我們把其中的1 1/4換成k,設正方形一边长
Some flat geometry topics, changing their conditions or conclusions etc, lead to new conclusions. If we conscientiously and often mentor students to think in this regard in geometry teaching, it is good for them to cultivate their logical arguments and their ability to work independently. Here are some ways to introduce. First, change the number of questions for the alphabet, introduced a law. Some of the geometry questions argue or deduce the numerical relationship between fields, and if the numbers are replaced with letters, the general law of the change of the subject and the new relationship in the diagram can be found out. In this way, the study of individual and special graphics can be used as a general study of the same type of question. For example, there is a question: “Make a rectangle and a known square equi-square, and make the perimeter of the rectangle equal to 1 1/4 times the known perimeter of the square.” Let's replace 1¼ with k, Long side