论文部分内容阅读
听课中,多次碰到这样一个问题:有些教师对教材中的相似三角形的定义产生异议。他们把相似三角形的定义:“两个对应角相等,对应边成比例的三角形,叫做相似三角形”中的“两个”理解成是用来修饰“对应角”的,而不是修饰“三角形”的,按这样的理解,就把相似三角形的定义讲授成:有两个对应角相等,(三条)对应边成比例的(两个)三角形,叫做相似三角形。而教材中相似三角形定义的原意,“两个”显然是指两个三角形,这从教材中引出定义前的观察、测量两个三角形的过程,以及定义引出后,应用定义证明三角形相似的例题中,都可得到证实,究其产生异议的原因,是对定义的叙述句式有不同的看法。他们为了说明“两个”是修饰“对应角”的,往往把三角形内角和定理及相似三角形的判定定理作为根据:
In the course of lectures, we encountered such a problem several times: Some teachers objected to the definition of similar triangles in textbooks. They consider the definition of similar triangles as “two equals” whose two corresponding angles are equal, the triangles that are proportional to the sides, called similar triangles, are understood to be used to modify “corresponding angles” rather than modifying the “triangles”. According to this understanding, the definition of a similar triangle is taught as follows: There are two corresponding angles equal, and (three) proportional triangles (two) are called similar triangles. The original meaning of the similar triangle definition in the textbook, “two” obviously refers to two triangles, which leads from the textbook to the process of defining the observation, measuring the two triangles, and after the definition is exported, the application definition proves that the triangles are similar in the example Can be confirmed, and the reason for their disagreement is that they have different opinions on the descriptive sentence structure. In order to show that “two” is to modify the “corresponding angle,” they often base the triangular inner angle and theorem and the similarity triangle’s decision theorem on: