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高考数学立体几何解题思路和技巧;
发布时间: 2019-01-15 | 来源:未知 |  本文被阅读 次
高考数学立体几何解题思路和技巧;
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高考立体几何试题一般共有4道(选择、填空题3道,解答题1道),共计总分27分左右,考查的知识点在20个以内。选择填空题考核立几中的计算型问题,而解答题着重考查立几中的逻辑推理型问题,当然,二者均应以正确的空间想象为前提。随着新的课程改革的进一步实施,立体几何考题正朝着“多一点思考,少一点计算”的发展。
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  高考数学立体几何解题技巧
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  1.有关平行与垂直(线线、线面及面面)的问题,是在解决立体几何问题的过程中,大量的、反复遇到的,而且是以各种各样的问题(包括论证、计算角、与距离等)中不可缺少的内容,因此在主体几何的总复习中,首先应从解决“平行与垂直”的有关问题着手,通过较为基本问题,熟悉公理、定理的内容和功能,通过对问题的分析与概括,掌握立体几何中解决问题的规律--充分利用线线平行(垂直)、线面平行(垂直)、面面平行(垂直)相互转化的思想,以提高逻辑思维能力和空间想象能力。
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  2.判定两个平面平行的方法:
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  (1)根据定义--证明两平面没有公共点;
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  (2)判定定理--证明一个平面内的两条相交直线都平行于另一个平面;
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  (3)证明两平面同垂直于一条直线。
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  3.两个平面平行的主要性质:
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  ⑴由定义知:“两平行平面没有公共点”。
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  ⑵由定义推得:“两个平面平行,其中一个平面内的直线必平行于另一个平面。
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  ⑶两个平面平行的性质定理:”如果两个平行平面同时和第三个平面相交,那么它们的交线平行“。
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  ⑷一条直线垂直于两个平行平面中的一个平面,它也垂直于另一个平面。
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  ⑸夹在两个平行平面间的平行线段相等。
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  ⑹经过平面外一点只有一个平面和已知平面平行。
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  以上性质⑵、⑷、⑸、⑹在课文中虽未直接列为”性质定理“,但在解题过程中均可直接作为性质定理引用。
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Generally, there are four solid geometry questions in the college entrance examination (3 choices, 3 filling-in questions and 1 answer question). The total score is about 27 points, and the knowledge points examined are less than 20. Choose the computational questions in the test of filling in the blanks, and focus on the logical reasoning questions in the test of solving the questions. Of course, both of them should take the correct spatial imagination as the premise. With the further implementation of the new curriculum reform, three-dimensional geometry examination questions are developing towards "more thinking, less calculation".
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The Skills of Solving Mathematical Three-dimensional Geometry Problems in College Entrance Examination
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1. Parallel and vertical (line, line and surface) problems are encountered repeatedly in the process of solving solid geometry problems, and are indispensable to various problems (including demonstration, calculation angle, distance, etc.). Therefore, in the general review of main geometry, we should first start with solving the problems related to "parallel and vertical", through comparison. In order to understand the content and function of axioms and theorems, through the analysis and generalization of the problems, we can grasp the law of solving problems in solid geometry - making full use of the ideas of line parallel (vertical), line parallel (vertical), plane parallel (vertical) mutual transformation, so as to improve the logical thinking ability and spatial imagination ability.
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2. The method of determining the parallel of two planes:
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(1) According to the definition, it is proved that there is no common point in the two planes.
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(2) Decision Theorem - Prove that two intersecting lines in one plane are parallel to the other plane;
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(3) Prove that the two planes are perpendicular to a straight line.
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3. The main properties of two parallel planes:
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(1) According to the definition, there is no common point in two parallel planes.
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Click View: More College Entrance Examination Answer Skills
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(2) The definition deduces: "Two planes are parallel, and the straight line in one plane must be parallel to the other plane.
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(3) The property theorem of two parallel planes: "If two parallel planes intersect with the third plane at the same time, then their intersection lines are parallel".
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(5) A straight line is perpendicular to one of the two parallel planes, and it is also perpendicular to the other.
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(5) Parallel lines clamped between two parallel planes are equal.
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_There is only one plane parallel to the known plane passing through an out-of-plane point.
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Although the above properties (_, _, _, _) are not directly listed as "property theorems" in the text, they can be directly cited as property theorems in the process of solving problems.
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