矩形、菱形慎判断

• 作 者: 王锋
• 出 处: 中学生数理化(八年级数学)(配合人教社教材)
• 发表日期: 2013年04期
• 关键词: 分类讨论 题设 错解 位线 角边角 邻边 可能情况 引以为鉴 石召

一些同学在初学矩形、菱形的知识时,会由于基础知识掌握不牢,分类讨论意识不强而出现错误.现就常见误区举例剖析如下,望同学们能引以为鉴.例1如图1,顺次连接四边形ABCD各边中点得到四边形EFGH.要使四边形EFGH为矩形,应添加的条件是().A.AB//DC B.AB=DCC.AC⊥BD D.AC=BD错解:选D.剖析:由于审题不严,以为对角线相等的四边形是矩形,从而选D,导致错解.事实上,要判断的是四边形EFGH,而不是四边形ABCD.此外,对角线相等的四边形也不一定就是矩形.

Some students in the beginning of the rectangular, diamond-shaped knowledge, due to lack of basic knowledge of mastery, classification of the lack of awareness and mistakes are now common mistaken examples as follows, hope students can learn from them. , Connect the middle of each side of the quadrilaterals ABCD to get the quadrilateral EFGH. To make the rectangle EFGH rectangular, the condition to be added is () .A.AB // DC B.AB = DCC.AC⊥BD D.AC = BD Solution: Select D. Analysis: Due to the lax trial, that quadrilateral diagonals are rectangular, so choose D, leading to misinterpretation. In fact, to determine the quadrilateral EFGH, rather than the quadrilateral ABCD. In addition, the diagonal The same quadrilateral is not necessarily rectangular.