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86年(上海)高考理工类最后一道试题是: 已知直角三角形ABC的两直角边AC=2,BC=3,P为斜边AB上一点(图1)。现沿CP将此直角三角形折成直二面角A-CP-B,当AB=7~(1/2)时,求二面角P-AC-B的大小。以立几作为高考试题的压阵题是第一次,对此可能有不同看法,但对如强空间想像力的考查,无疑会起积极作用。本文拟就对此题的分析,谈谈对空间想像能力的认识。这一题的困难在于如何从平面图作出立体图以及如何作出二面角P-AC-B的平面角。对于空间想像力较差的学生,往往感到无从着手。本题解法很多,但关键都在二面角P-AC
The last question in the 86th (Shanghai) college entrance examination science and engineering class is: The right-angled triangle ABC has two right-angled edges AC=2, BC=3, and P is a point on the hypotenuse AB (Figure 1). This straight triangle is now folded along the CP into a straight dihedral angle A-CP-B. When AB=7~(1/2), the dihedral angle P-AC-B is obtained. It is the first time that Li Lai has been the subject of a high-level exam question. This may have different views on it, but the examination of a strong spatial imagination will undoubtedly play an active role. This article proposes to discuss the issue of space imagination. The difficulty of this problem lies in how to make a perspective view from the floor plan and how to make the planar angle of the dihedral angle P-AC-B. Students with poor spatial imagination often feel that they cannot start. There are many solutions to this problem, but the key is the dihedral P-AC.