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www.hg5793.com:高一数学苏教版必修2教学案第1章6空间两条直线的位置关系(2)

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江苏省泰兴中学高一数学教学案() 必修 空间两条直线的位置关系() 班级 姓名 目标要求 1、 理解异面直线的定义,异面直线所成角的定义、两条异面直线垂直的定义; 2、 理解异面直线判定的方法,并会求简单的异面直线所成角; 、体会空间问题化归为平面问题求解的策略. 重点难点 重点:异面直线的判定及异面直线所成角的定义; 难点:异面直线所成角的定义和范围. 典例剖析 例、()在空间四边形中,直线与位置关系是. ()下列命题中 ①已知a,b,c三条直线,其中a,b异面,若ac,则b与c异面 ②若a与b异面,b与c异面,则a与c异面 ③分别在两个平面内的直线一定是异面直线 ④既不平行也不相交的两条直线是异面直线 正确命题的序号是. 例、如图,已知 直线相交. 是异面直线, ,求证:直线 中至少有一条与 例、如图,已知不共面的直线 相交于点是直线上两点分别是上一点.求证是异面直线. 例、如图,已知 是棱长为的正方体 (1) 正方体的哪些棱所在的直线与直线 是异面直 线? (2) 求异面直线 与所成的角; (3) 求异面直线 和所成的角. D1 A1 C1 B1 D A C B 学习反思 、反证法的一般步骤是; 、求异面直线所成角的关键是,如何作出异面直线所成角? 课堂练习 、给出下列命题 () 则和是异面直线 ()与异面与异面,则与异面 ()不同在一个平面内,则与异面 ()不同在一个任何平面内,则、异面 正确命题的序号是. 、设两条异面直线所成角为θ ,则角θ 的范围是 . 、在棱长为的正方体 中,则 与 成角为. 、在两个相交的平面内各画一条直线,使它们成: ()平行直线; ()相交直线; ()异面直线. 江苏省泰兴中学高一数学作业() 班级 姓名得分 、一条直线和两条异面直线的一条平行,则它与另一条的位置关系是 、已知四棱柱 ,与棱异面的棱有. 、下列命题中,正确的命题序号是. ① ,直线 ,则 所成的角为; ②若直线 ,且 所成的角为,则 所成的角也为; ③若直线 与直线所成的角相等,则 ; ④若直线 与直线所成的角不相等,则 不平行. 、若 ,直线 ,和异面,则和所成的角为. 、正方体的棱长为a,那么 (1)哪些棱所在的直线与直线成异面直线. (2)直线与所成角的大小为 . ()直线与所成角的大小 . 、正方体 中,、分别是棱、的中点,则与所成的角为 、分别和两条异面直线 都相交的两直线 的位置关系是 、 是异面直线,,,,是四个不同的点,且 求证:与是异面直线. . . 、如图,空间四边形中,,分别是边、的中点,空间四边形的两条对角线、的长均为, ()若,求两条对角线、所成的角的大小. () 若,求两条对角线、所成的角的余弦值. 、如图,在正方体 所成角的大小. 中, ,、分别是、的中点,求异面直线 与 D1 A1 C1 B1 D A F B C E

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