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以能力立意、极富思维含量的几何开放探究题频频出现在中考中.这类试题不仅承载着对学生基础知识和技能的理解和掌握、基本数学思想的领悟、基本数学活动经验的形成等诸多方面进行评价的功能,更能间接而有效地考查学生“数学地思维”的广度与深度.下面就一道中考几何探究题予以解法探讨、变式和思考,供参考.题目:(2013年江西省)某数学活动小组在作三角形的拓展图形,研究其性质时,经历了如下过程:
With the conception of ability, highly thought-finding geometric open questions frequently appear in the middle school entrance exams.This type of questions not only carries the understanding and mastery of students’ basic knowledge and skills, the comprehension of basic mathematical thought, the formation of basic mathematical activity experience and many other Evaluation of the function, the more indirect and effective examination of students “mathematical thinking ” the breadth and depth below to explore a discussion of the geometry of the exam to explore the problem, variants and thinking for reference. Title: (2013 Jiangxi Province) A mathematical activity group in the triangle to expand the graphics, the study of its nature, has gone through the following process: