论文部分内容阅读
立体几何中求两条异面直线的距离和求两个平面的二面角的问题往往是比较困难的.这里介绍两个定理,可作为解以下两道立体几何问题的依据.定理1.两条异面直线 a、b 的距离,就是 a 到过 b 而平行于 a 的平面的距离.定理2.两个平面间的二面角的平面角与两平面的垂线所成的角相等或互补.这两定理的证明不难,请读者自证.一、下面首先介绍求两条异面直线距离的三种方法.已知:三棱锥 S-ABC,底面是边长为4 2~(1/2)的正三角形,棱 SC 的长为2,且垂直于底面,E、D 分别为 BC、AB 的中点.
The problem of finding the distance of two non-planar straight lines and finding the dihedral angle of two planes in three-dimensional geometry is often difficult. Two theorems are introduced here, which can be used as the basis for solving the following two-dimensional geometric problems. Theorem 1. Two The distance between the straight lines a, b is the distance from a to b and parallel to the plane of a. Theorem 2. The plane angle between dihedral angles between two planes is equal to the angle formed by the perpendicular lines on two planes or Complementary. The proof of these two theorems is not difficult, please readers self-certification. First, the following introduces the three methods to find the distance between two different straight lines. Known: triangular pyramid S-ABC, the bottom side is 4 2 ~ ( 1/2) of the regular triangle, the length of the rib SC is 2 and perpendicular to the bottom surface, E, D are the midpoints of BC, AB, respectively.