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中学数学各分科知识的联系和借鉴是发展学生综合能力的重要基石,初中教学平几后,数、形结合的综合训练就有了条件。下面就代数运算对平几证题的积极作用作些归纳梳理,供参考。一、用字母表示有关的几何量平几证题中,有时结论表为数量关系的代数式,若能恰当地选择字母表示其中的有关量,就能借助代数式运算之便完成证明。例1 矩形ABCD中,AD=2~(1/2)AB。以AD为直径在形外作半圆,P为半圆周上任意一点,连PB、PC分别
The connection and reference of high school mathematics in each sub-discipline is an important cornerstone for the development of students’ comprehensive abilities. After a few years of teaching in junior high schools, comprehensive training in combination of numbers and forms will be available. The following is a summary of the positive effects of algebraic operations on a few proofs for reference. First, use the letters to indicate the relevant geometric quantity. In some cases, sometimes the conclusion table is an algebraic formula of the quantity relation. If the letters can be properly selected to represent the relevant quantities, the algebraic operation can be used to complete the proof. Example 1 In the rectangular ABCD, AD=2~(1/2)AB. Taking AD as the diameter for semicircle outside the shape, P for any point on the half circle, even PB, PC respectively