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662882ocm:异面直线所成角导学案10

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2013——2014 高一 数学必修 2 导学案

编制人:

编号:10

年级:高一

班级:

小组:

姓名:

教师评价:

课题:空间中直线与直线的位置关系(2)
【学习目标】 1.知识与能力:1.理解等角定理 2.理解空间异面直线所成角的定义、范围,并会作出、求出 简单异面直线所成角。 2.过程与方法:通过小组合作探究得出空间异面直线所成角的定义、范围,并会作出、求出 简单异面直线所成角, 培养学生的识图、作图能力及空间想象能力。 3.情感态度价值观:在对学生进行创造性思维培养的同时,激发学生对科学文化知识的探 求热情。 【使用说明与学法指导】 1.自学教材 P46—P47,划出重要知识,联系课本知识和学过的知识规范完成学案自主学 习内容并记熟基础知识。 2.小组合作、讨论完成学案合作探究内容;组长负责,拿出讨论结果,准备展示、点评。 自主学习: 1、求角的大小的方法:① ② 2、异面直线的定义: 思考: 异面直线所成角的范围: 两条直线垂直定义: 3、对于两条相交直线,用 线的 倾斜程度) ;在空间中用 你的疑惑之处: ;包括 垂直和 垂直

1、正四面体 ABCD 中, E 为 BC 边中点, 求 AE 与 BD 所成角的余弦值。

A

B E C

D

2、在正方体 ABCD ? A1 B1C1 D1 中求 AD1 与 A1C 所成的角 D1 A1 刻画他们的相对位置(一条直线相对于另一条直 刻画两异面直线的相对位置 D C B1

C1

合作探究:

当堂检测:

教师寄语: 业精于勤荒于嬉,行成于思毁于随

1

2013——2014 高一 数学必修 2 导学案

编制人:

编号:10

年级:高一

班级:

小组:

姓名:

教师评价:

探究二、求异面直线所成角 例 1、在正方体 ABCD ? A1 B1C1 D1 中(1)求 AA1 与 BC 所成的角; (2)求 AA1 与 BC1 所成 的角(3)求 AA1 与 BD1 所成角的余弦值(4)E 为 CD 的中点,求 A1C 与 BE 所成角的余弦值。 (仔细阅读课本 P46 例 3,按照作、证、算、答四步求角) A1 D1 B1 C1

例 2、空间四边形 ABCD 中, AD ? BC ? 2 , E , F 分别是 AB, CD 的中点, EF ? 3 , 求异面直线 AD, BC 所成的角。

A E
D C

B
A B

D F C

( C

层 选 做 ) 拓 展 : 已 知 长 方 体

ABCD — — ?1?1C1 D1 中 ,

?? ? 2 3 , ?D ? 2 3, ??1 ? 2,
(1) BC 和 ?1C1 所成的角是多少度? (2) ?? 1 和 ? C1 所成的角是多少度?

归纳小结:

教师寄语: 业精于勤荒于嬉,行成于思毁于随

2


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