数学精英解立体几何题（Mathematical elite solving the problem of solid geometry）.doc

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数学精英解立体几何题（Mathematical elite solving the problem of solid geometry）.doc

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数学精英解立体几何题（Mathematical elite solving the problem of solid geometry）

数学精英解立体几何题（Mathematical elite solving the problem of solid geometry） (9) mathematics elite solves the problem of solid geometry 1. (2007 Hubei volume fourth) there are two straight lines outside the plane alpha, m and n. If the projection of M and N in plane alpha is m and N, respectively, the following four propositions are given: The M n m group n; group II m n m n t t M and n intersect, m and N intersect or coincide; m and n parallel, m and N parallel or overlap The number of incorrect propositions is A.1 B.2 C.3 D.4 [analysis] D in classroom space is a cuboid model, m n, the ground wall line, m, N on the wall, namely M n is an anomalous m n is not necessary but not sufficient condition. Therefore, the.M is a false proposition, n m, intersecting or parallel, so the n can be different; the proposition is false. [description] Abstract line (surface) relationship specific. Is to find the space model, rectangular classroom is a few models without cost. When necessary, candidates can also the hands of the ruler and the triangle graphic combination. 2. (2007 Beijing volume third) a sufficient condition of plane plane is alpha, beta A. is a line of a, a, a, alpha, beta B. is a line of a, AA, beta C. there are two parallel lines a, B, a, a, B, alpha beta. D. there are two lines in different planes of a, B, a, a, B, alpha beta. [analysis] D takes the ceiling of the examination room and a wall as the alpha and beta to find the different lines a, B meets A, B, and C, thus excluding the first three [description] the classroom itself is a good cuboid model, we determine the line line, line relationship with it, simple and clear. 3. (2007 Hunan volume eighth) for 8 vertices and 1 edges of the cube on the ball surface, are edges, the midpoint of the line is straight line was truncated by the long ball (for) A. B. C. D. [analysis] D intercept plane circular surface of the radius of the, The line segment picked by the ball O is the diameter of the circle, so D. is chosen [instru