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文[1]对于三角形中的线共点问题给予了解析证明,读后颇受启发。但因中所述三线共点和三点共线的充要条件的两定理(Ceva定理、Menelaus定理)其条件的必要性正是初中平几教材中的两习题,该文对这两定理的条件必要性的证明都采用反证法并运用条件的充分性而获证.而条件充分性的证明,又都超出了初中知识范围.从指导教学出发,这对引导初中学生运用解析几何知识解决平几中的有关问题,似有一定距离.
The paper [1] gives an analytical proof of the line co-point problem in the triangle, which is quite inspiring after reading. However, the necessity of the two theorems (Ceva’s theorem and Menelaus’s theorem) of the necessary and sufficient condition of the three-line common point and the three-point collinearity are the two exercises in the junior middle school textbook. This paper deals with two theorems. The proof of the necessity of the conditions are all obtained by using the anti-evidence method and using the adequacy of the conditions. The proof of the sufficient condition of the conditions is beyond the scope of the junior high school knowledge. Starting from the instructional teaching, this guides junior high school students to use analytical geometry to solve the problem. There seems to be a certain distance in the relevant issues.