题目三棱柱ABC-A_1B_1C_1的所有棱长都相等,AA_1⊥平面ABC,A_1B交AB_1于点O,D为棱CC_1的中点.(1)求证:OD∥平面ABC;(2)求证:AB_1⊥平面A_1BD.本题是立体几何的一道常规题,难度不大.主要考察棱柱、直线与平面的位置关系等基础知识,并以此为依托考察学生的空间想象能力、逻辑思维能力.重点考察直线与平面平行、垂直的判定定理. Title Triangular prism ABC-A_1B_1C_1 all the same edge length, AA_1⊥ plane ABC, A_1B intersection AB_1 at point O, D is the midpoint of the edge CC_1 (1) verify: OD∥ plane ABC; (2) verify: AB_1 Plane A_1BD This topic is a regular topic of solid geometry, not difficult, mainly to study the basic knowledge of the prism, the relationship between the position of the line and the plane, and based on this to examine students’ spatial imagination ability and logical thinking ability. Plane parallel, vertical decision theorem.