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线段的和差问题是几何证明中常见的题型,它与证明线段相等紧密相联.一般来说,通过作辅助线可转化为线段相等问题.解决线段的和差问题,需要综合应用三角形全等,直角三角形斜边上的中线等于斜边的一半,含有30o角的直角三角形的性质,线段中垂线的性质,角平分线性质,三角形,梯形中位线性质等知识.因此,通过此问题的讨论,一方面,帮助学生对与之相关的知识、定理进行梳理,系统化,进而建构有效的知识系统;另一方面,使他们在学习具体的几何知识的同时,掌握“化归”的数学思想方法.
The problem of sum and difference of line segments is a common problem in geometric proof, which is equal and close to the proof line segment. In general, it can be transformed into the line segment equal problem by using the auxiliary line. To solve the sum-of-line problem of line segments, , Etc. The center line on the hypotenuse of the right triangle is equal to half of the hypotenuse and contains the knowledge of right angle triangle with 30o angle, the nature of the vertical line in the line, the nature of the angle bisector, the nature of the triangle and the trapezoidal median line, etc. Therefore, On the one hand, to help students to sort out and systematize the related knowledge and theorem, and then construct an effective knowledge system; on the other hand, they should learn the specific knowledge of geometry while at the same time "Mathematical method of thinking.