立体几何篇 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。从历年的考题变化看，以简单几何体为载体的线面位置关系的论证，角与距离的探求是常考常新的热门话题。 知识整合 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。 2、判定两个平面平行的方法： (1)根据定义--证明两平面没有公共点; (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; (3)证明两平面同垂直于一条直线。 3、两个平面平行的主要性质： (1)由定义知：“两平行平面没有公共点”。 (2)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。 (3)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“。 (4)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。 (5)夹在两个平行平面间的平行线段相等。 (6)经过平面外一点只有一个平面和已知平面平行。 以上性质(2)、(3)、(5)、(6)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。 解答题分步骤解决可多得分 01、合理安排，保持清醒。 数学考试在下午，建议中午休息半小时左右，睡不着闭闭眼睛也好，尽量放松。然后带齐用具，提前半小时到考场。 02、通览全卷，摸透题情。 刚拿到试卷，一般较紧张，不宜匆忙作答，应从头到尾通览全卷，尽量从卷面上获取更多的信息，摸透题情。这样能提醒自己先易后难，也可防止漏做题。 03、解答题规范有序。 一般来说，试题中容易题和中档题占全卷的80%以上，是考生得分的主要来源。 对于解答题中的容易题和中档题，要注意解题的规范化，关键步骤不能丢，如三种语言(文字语言、符号语言、图形语言)的表达要规范，逻辑推理要严谨，计算过程要完整，注意算理算法，应用题建模与还原过程要清晰，合理安排卷面结构……对于解答题中的难题，得满分很困难，可以采用“分段得分”的策略，因为高考阅卷是“分段评分”。 比如可将难题划分为一个个子问题或一系列的步骤，先解决问题的一部分，能解决到什么程度就解决到什么程度，获取一定的分数。 有些题目有好几问，前面的小问你解答不出，但后面的小问如果根据前面的结论你能够解答出来，这时候不妨引用前面的结论先解答后面的，这样跳步解答也可以得分。
Mathematics Answering Skills in College Entrance Examination in 2019: Stereo Geometry Solution
There are generally four three-dimensional geometry questions in the National College Entrance Examination (3 choices, 3 filling-in questions and 1 answer question). The total score is about 27, 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". From the change of examination questions over the years, the demonstration of the relationship between line and surface position with simple geometry as the carrier, and the exploration of angle and distance are often new hot topics in the examination. Knowledge integration 1. The problems of parallel and vertical (line, line and surface) 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, the first step is to solve the problems related to parallel and vertical. Beginning with the basic problems, we are familiar with the contents and functions 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-line parallel (vertical), line-plane parallel (vertical) and plane-plane parallel (vertical) mutual transformation, so as to improve the logical thinking ability and spatial imagination ability. 2. The method of judging the parallel of two planes: (1) According to the definition - proving that there is no common point in two planes; (2) the judgment theorem - proving that two intersecting lines in one plane are parallel to another plane; (3) proving that two planes are perpendicular to a straight line. 3. The main properties of two parallel planes: (1) According to the definition, there is no common point in two parallel planes. (2) It is deduced from the definition that "two planes are parallel, and the straight line in one plane must be parallel to the other plane." (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". (4) A straight line is perpendicular to one of the two parallel planes, and it is also perpendicular to the other plane. (5) Parallel lines clamped between two parallel planes are equal. (6) There is only one plane parallel to the known plane passing through an out-of-plane point. Although the above properties (2), (3), (5), (6) are not directly listed as "property theorems" in the text, they can be directly cited as property theorems in the process of solving problems. To solve the problem step by step, we can score more than 01 points, arrange reasonably and keep awake. Mathematics exam in the afternoon, it is recommended to rest for about half an hour at noon, sleepless or closed eyes, try to relax. Then bring all the appliances and come to the examination hall half an hour in advance. 02. Overview the whole volume and find out the situation. Just got the test paper, generally more nervous, not in a hurry to answer, should go through the whole volume from beginning to end, try to get more information from the surface of the paper, find out the situation. This can remind oneself that it's easy before it's difficult, and it can also prevent missing out on the topic. 03. Standardized and orderly answers. Generally speaking, easy questions and mid-range questions account for more than 80% of the total volume, which is the main source of candidates'scores. For easy and medium-sized questions, attention should be paid to the standardization of problem solving, and the key steps should not be lost. For example, the expression of three languages (literal language, symbolic language, graphic language) should be standardized, logical reasoning should be rigorous, the calculation process should be complete, the arithmetic algorithm should be paid attention to, the process of modeling and restoring application problems should be clear, and the paper structure should be reasonably arranged. It is very difficult to get a full score for solving the difficult questions. We can adopt the strategy of "piecewise score", because the marking of college entrance examination papers is "piecewise score". For example, the problem can be divided into a sub-problem or a series of steps, first solve a part of the problem, can solve to what extent, get a certain score. There are several questions in some questions, but you can't answer the questions in the front, but if you can answer the questions in the back according to the conclusions in the front, you may as well use the conclusions in the front to answer the questions in the back first, so that the jump solution can also score.