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今年高考数学试题中的第23题(文理科同)是一道立体几何题,题目如下:如图1,在三棱锥S-ABC中,SA底面ABC,ABBC。DE垂直平分SC,且分别交AC、SC于D、E。又SA=AB,SB=BC。求以BD为棱,以BDE与BDC为面的二面角的度数。本题旨在“考查直线和平面,直线和直线的位置关系,二面角等基本知识,以及逻辑推理能力和空间想象能力”,题中已知条件,既有线线的垂直关系,又有线面的垂直关系,还有线段之间的度量关系,知识复盖面大,解法灵活多样,既有一定难
This year, the 23rd question in the mathematics question of college entrance examination (the same with arts and sciences) is a three-dimensional geometry question, the title is as follows: In Figure 1, in the triangular pyramid S-ABC, SA bottom ABC, ABBC. DE divides the SC vertically and sends AC and SC to D and E, respectively. SA=AB, SB=BC. Find the degree of dihedral angle with BD as the edge and BDE as BDC. This question aims to “examine the relationship between straight lines and planes, positional relationships between straight lines and straight lines, dihedral angles and other basic knowledge, as well as logical reasoning capabilities and spatial imagination capabilities”, the known conditions in the title, the vertical relationship between the two lines, and the line surface The vertical relationship, as well as the metric relationship between line segments, large coverage of knowledge, flexible and diverse solution, it is difficult