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对学生能力的培养,越来越受到人们的重视。因此,近年来中考的开放性、探索性试题日渐增多,对学生能力考察的要求越来越高。故而在中学数学教学中,加强发散思维的训练,做到一题多解,一题多变,对发展学生智力、培养学生能力起着十分重要的作用。现就初三几何中第144页的例4,谈谈一题多解、一题多变的粗浅做法。如图1,⊙O_1与⊙O_2外切于点 A,BC 是⊙O_1和⊙O_2的公切线,B、C 是切点,求证:AB⊥AC。
The cultivation of student abilities has received increasing attention from people. Therefore, in recent years, the open and exploratory examination questions of the entrance examination have been increasing day by day, and the requirements for the examination of students’ ability have become higher and higher. Therefore, in the teaching of middle school mathematics, the training of divergent thinking is strengthened. There are many solutions to this problem, and there is a lot of variation in one question, which plays an important role in the development of students’ intelligence and ability to develop students. Now, on the third page of the third-generation geometry, on page 144, we will talk about the topical and multi-level approaches. As shown in Figure 1, ⊙O_1 and ⊙O_2 are circumscribed at point A, BC is the common tangent of ⊙O_1 and ⊙O_2, and B and C are tangent points. Prove that: AB⊥AC.