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一题多解能开拓学生的思路,训练学生的发散思维。如果抓住典型命题,通过分析找出命题之间的内在联系,进行类比、归纳、总结,找出多个同类命题的统一解题思路,往往能达到举一反三,触类旁通的效果,所以多题一解是培养学生解题能力的一个重要手段,也是培养学生分析判断能力的一个途径。例1 已知AC⊥AB,BD⊥AB,AD和BC相交于E,EF⊥AB,垂足为F,又AC=p,BD=q,EF=r,AF=m,FB=n ①用m、n表示r/p, ②用m、n表示r/q, ③求证:r/p+r/q=1 (现行初中几何课本第一册第200页第7题)
A multi-explanation can open up students’ ideas and train students’ divergent thinking. If you grasp the typical propositions, find out the intrinsic links between propositions through analysis, and conduct analogies, inductions, summaries, and find out the same problem-solving ideas for multiple propositions of the same type, you can often achieve the effect of analogy and by analogy, so the multi-question solution It is an important means of cultivating students’ ability to solve problems, and it is also a way to train students to analyze and judge their abilities. Example 1 It is known that AC ⊥ AB, BD ⊥ AB, AD and BC intersect at E, EF ⊥ AB, pedestal is F, and AC=p, BD=q, EF=r, AF=m, FB=n 1 m, n denotes r/p, 2 denotes m/n, r/q, 3 Proof: r/p+r/q=1 (current junior high school geometry textbook volume 1 page 200, item 7)