论文部分内容阅读
立体几何是高中数学中极为重要的知识点,是高考必考的内容之一.本文以2012年湖南理科数学试题第18题为例,说明如何用传统的几何方法和向量法来解决立体几何题.如图1,在四棱锥P-ABCD中,PA⊥平面ABCD,AB=4,BC=3,AD=5,∠DAB=∠ABC=90°,E是CD的中点.(1)证明:CD⊥平面PAE;(2)若直线PB与平面PAE所成的角和PB与平面ABCD所成的角相等,求四棱锥P-ABCD的体积.
Three-dimensional geometry is an extremely important knowledge in high school mathematics, is one of the college entrance examination will be one of the content.In this paper, 2012 Hunan Science Mathematics test questions 18 as an example, how to use traditional geometric methods and vector method to solve the problem of three-dimensional geometry As shown in Fig. 1, in the pyramid P-ABCD, PA⊥ plane ABCD, AB = 4, BC = 3, AD = 5, ∠DAB = ∠ABC = 90 ° and E is the midpoint of CD. : CD⊥ plane PAE; (2) If the angle formed by the line PB and the plane PAE and the angle formed by PB and the plane ABCD are equal, find the volume of the quadrangular pyramid P-ABCD.