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解答数学题的叙述形式不可能千篇一律,但叙述表达必须合乎逻辑,准确恰当,条理清楚,简洁明了。当前有的师生认为解数学题在于“多亦求多”,常常不顾基本的逻辑层次,存在着表达不够合理的现象,从而影响到解题的质量。下面仅举几例以作分析。例1 设三棱锥v—ABC中,∠AvB=∠BvC=∠CvA=Rt∠,求证:△ABC是锐角三角形。下面是一位同学给出的证法。证如图1 设∠vAC=a,∠vAB=β,则根据《立体几何》p145第3题的结论可得cos A=cosa·cosβ(·)而a、β都是Rt△的内角, ∴ cosa>o,cosβ>0,从而COSA>0,同理可证
The narrative form of answering a mathematics question cannot be stereotyped, but the narrative expression must be logical, accurate and appropriate, clear and concise. At present, some teachers and students think that the solution to mathematics problems lies in “more and more”, often ignoring the basic level of logic, and the phenomenon of unreasonable expression, which affects the quality of problem solving. Only a few examples are given below for analysis. Example 1 In the triangular pyramid v-ABC, ∠AvB=∠BvC=∠CvA=Rt∠. Verify that ΔABC is an acute triangle. Here is the proof given by a classmate. As shown in Fig. 1, let ∠vAC=a and ∠vAB=β, and then according to the conclusion of the “Solid Geometry” p145 question 3, we can get cos A=cosa·cosβ(·) and a and β are internal angles of Rt △. Cosa>o, cosβ>0, thus COSA>0, the same token