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数学的基本特点之一是严谨性,它除了要求数学结论必须精炼准确外,更要求对结论的推理论证既严格又周密,几何教学的任务之一是培养学生的逻辑思维能力,为此,在几何教学中尤其要注意其严谨性,不能凭直觉和想象推理,本文例举几个似是而非的几何问题加以说明。 问题1:面积相等的两个三角形不一定全等,周长相等的两个三角形也不一定全等,但周长和面积分别相等的两个三角形一定全等吗?
One of the basic characteristics of mathematics is rigorousness. In addition to requiring that mathematical conclusions must be refined and accurate, it also requires that the theoretical proofs of conclusions are both strict and thorough. One of the tasks of geometry teaching is to cultivate students’ logical thinking ability. For this reason, In geometry teaching, we must pay special attention to its rigorousness. We can’t rely on intuition and imaginary reasoning. This article gives some examples of plausible geometric problems to illustrate. Question 1: The two triangles with equal area are not necessarily equal, but the two triangles with the same perimeter are not necessarily equal, but are the two triangles with equal circumference and area equal to each other?