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在教学圆周角定理证明时,几乎没有一个学生就结论的证明进行分类说明,大都只是在教师分好类的基础上分别进行证明结论而已.事实上,学生在之前的数学学习中已经接触了大量的分类思想,为什么对此定理的证明时就缺少分类的意识呢?我们不妨先看一下圆周角定理证明中的分类方式特点.一、圆周角定理的证明特点圆周角定理:圆周角的度数等于同弧所对圆心角度数的一半.教材对此定理证明一般都按下列分类进行:i.当圆心O在圆周角∠APB一边上时(图1.1).
Few students classify the conclusions of the proofs when teaching the theorems of circumferential angle theorems, most of them only prove the conclusions on the basis of the teachers’ sub-classifications. In fact, the students have been exposed to a great deal of previous mathematics learning We can first take a look at the classification of circular angle theorem in the proof of features. First, the proof of the circular angle theorem Features of the circular angle theorem: the degree of circular angle equal to The same arc as the center of the angle of half of the textbook theorem proved to be generally carried out according to the following categories: i. When the center of the circle O at the corner angle ∠ APB side (Figure 1.1).