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《中小学数学》(初中版)2011年第5期刊登了贺静的《一个常用的基本图形》一文,该文给出了一个常用的基本图形在证明时的应用,即“直角三角形斜边上的中线等于斜边的一半”这个基本图形文中还给出了3个例题,以说明该基本图形在证明时的应用.前两个例题的确很典型,因为我也正教初二,在讲解矩形性质时讲到了这个基本图形,但是读到例3时,我觉得这个例题并不典型,因为该例也可以利用三角形中位线定理以及全等的知识来证明,而且比利用此基本图形的方法更简便,学生也更容易理解.具体证明如下:
Mathematics for Primary and Secondary Schools (Junior High School Edition) published in issue 5 of He Jing’s “A Common Basic Graphic” in the 5th issue of 2011. This article gives an application of a commonly used basic figure in proofs, namely, “a right-angled triangle oblique”. The middle line on the side is equal to half of the hypotenuse. There are also 3 examples in this basic graphic text to illustrate the application of the basic figure in the proof. The first two examples are indeed typical because I also teach the 2nd This basic figure was mentioned when we talked about the nature of rectangles, but when we read Example 3, I think this example is not typical, because this example can also be proved by using the triangle’s median line theorem and the knowledge of the whole, and it is better than using this basic figure. The method is simpler and easier for students to understand. The concrete proof is as follows: