也谈两直线平行的充要条件

• 作 者: 黄殷
• 机 构: 广东省广州市广东番禺中学,
• 出 处: 中学生数学
• 发表日期: 2012年21期
• 关键词: 交流讨论 文中 截距

《中学生数学》2012年第5期刊登了《两直线平行的充要条件》一文(下称文[1]),文中作者指出两直线l1,l2的方程分别为:A1x+B1y+C1=0(其中A1,B1不同时为零),A2x+B2y+C2=0(其中A2,B2不同时为零),l1与l2平行的充要条件不是A1B2-A2B1=0且A1C2-A2C1≠0,也不是A1B2-A2B1=0且B1C2-B2C1≠0,更不是A1B2-A2B1=0且A1C2-A2C1≠0且B1C2-B2C1≠0.那么,两直线平行的充要条件究竟是什么?文[1]中没有给出.

“Secondary School Mathematics” 2012 the fifth issue of the “two necessary and sufficient conditions of parallel lines,” a text (the following article [1]), the author pointed out that the two lines l1, l2 equations were: A1x + B1y + C1 = 0 (Where A1 and B1 are not zero at the same time), A2x + B2y + C2 = 0 (where A2 and B2 are not zero at the same time), the necessary and sufficient condition for parallelism of l1 and l2 is not A1B2-A2B1 = 0 and A1C2- Nor A1B2-A2B1 = 0 and B1C2-B2C1 ≠ 0, but not A1B2-A2B1 = 0 and A1C2-A2C1 ≠ 0 and B1C2-B2C1 ≠ 0. What is the necessary and sufficient condition for the two lines to be parallel? ] Is not given.