论文部分内容阅读
初二学生对解代数习题比较熟悉,而对平面几何中的证明题多感困难。对于有的证明题,如能联想到代数解法就容易入手。例如证明b/a±d/c=1或b/a·d/c=1型的线段关系式,一般可通过引平行线,利用相似三角形的性质、三角形的面积公式等,转化为分母是同线段的分式或可以约分的分式进行运算。下面以初中《几何》第一册(1981年1月第1版)复习题四的几个题为例来说明。例1 OA是△OPQ的∠POQ的平分线,过A作AC∥QO,交OP于C。求证 OC/OP+OC/OQ=1。分析证式中二分式不同分母,考虑到
The second grade students are more familiar with the problem of solving algebraic exercises, but they are more troubled by the proofs in plane geometry. For some proving questions, it is easy to think of algebraic solutions. For example, it is proved that b/a±d/c=1 or b/a·d/c=1 refers to the line segment equation. Generally, it can be converted into a denominator by using the parallel triangles, using the properties of similar triangles, the area formula of the triangles, and so on. Fractions of the same segment or fractions that can be approximated are computed. The following is an example of the examination of several questions in the fourth volume of the junior high school “Geometry” Volume 1 (January 1981 first edition). Example 1 OA is the bisector of the ∠ POQ △ POQ, over A for AC ∥ QO, and OP for C. Prove OC/OP+OC/OQ=1. Analyze two different denominators in the proof, taking into account