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".
The Skills of Solving Mathematical Three-dimensional Geometry Problems in College Entrance Examination
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.
2. The method of determining the parallel of two planes:
(1) According to the definition, it is proved that there is no common point in the two planes.
(2) Decision Theorem - Prove that two intersecting lines in one plane are parallel to the other plane;
(3) Prove that the 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.
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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.
(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".
(5) A straight line is perpendicular to one of the two parallel planes, and it is also perpendicular to the other.
(5) Parallel lines clamped between two parallel planes are equal.
_There is only one plane parallel to the known plane passing through an out-of-plane point.
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.