2.2.1直线与平面平行判定公开课教案.pdf

2.2 直线、平面平行的判定及其性质教案3 课时2013-2014 下学期王文双一、教学目标：1、知识与技能1理解并掌握直线与平面平行的判定定理；2进一步培养学生观察、发现的能力和空间想象能力；2、过程与方法学生通过观察图形，借助已有知识，通过探索得出直线与平面平行的判定定理，并掌握直线与平面平行的判定定理及其灵活应用。3、情感、态度与价值观1让学生在发现中学习，增强学习的积极性；2让学生了解空间与平面互相转换的数学思想。二、教学重点、难点重点：直线与平面平行的判定定理及应用。难点：直线与平面平行的判定定理的探索及应用。三、学法与教学用具学法：学生借助实例，通过观察、思考、交流、讨论等，理解判定定理。教学用具：投影仪片四、教学过程设计一知识准备、新课引入提问 1：根据公共点的情况，空间中直线a 和平面有哪几种位置关系？并完成下表：(多媒体幻灯片演示)位置关系公共点符号表示图形表示我们把直线与平面相交或平行的位置关系统称为直线在平面外，用符号表示为 a提问 2：根据直线与平面平行的定义(没有公共点)来判定直线与平面平行你认为方便吗？谈谈你的看法，并指出是否有别的判定途径。二判定定理的探求过程1、直观感知提问：根据同学们日常生活的观察，你们能感知到并举出直线与平面平行的具体事例吗？生 1：例举日光灯与天花板，树立的电线杆与墙面。生 2：门转动到离开门框的任何位置时，门的边缘线始终与门框所在的平面平行(由学生到教室门前作演示)，然后教师用多媒体动画演示。2、动手实践教师取出预先准备好的直角梯形泡沫板演示：当把互相平行的一边放在讲台桌面上并转动，观察另一边与桌面的位置给人以平行的感觉，而当把直角腰放在桌面上并转动，观察另一边与桌面给人的印象就不平行。3、探究思考(1)上述演示的直线与平面位置关系为何有如此的不同？关键是什么因素起了作用呢？通过观察感知发现直线与平面平行，关键是三个要素：平面外一条线平面内一条直线这两条直线平行(2)如果平面外的直线a 与平面内的一条直线 b 平行，那么直线a与平面平行吗？进行证明4、归纳确认：多媒体幻灯片演示直线和平面平行的判定定理：平面外的一条直线与平面内的一条直线平行，则该直线和这个平面平行。简单概括：内外线线平行线面平行文档编码:CU8H5R6X9Q6 HV7R9M9V6J3 ZO6Z9A5Y9J8文档编码:CU8H5R6X9Q6 HV7R9M9V6J3 ZO6Z9A5Y9J8文档编码:CU8H5R6X9Q6 HV7R9M9V6J3 ZO6Z9A5Y9J8文档编码:CU8H5R6X9Q6 HV7R9M9V6J3 ZO6Z9A5Y9J8文档编码:CU8H5R6X9Q6 HV7R9M9V6J3 ZO6Z9A5Y9J8文档编码:CU8H5R6X9Q6 HV7R9M9V6J3 ZO6Z9A5Y9J8文档编码:CU8H5R6X9Q6 HV7R9M9V6J3 ZO6Z9A5Y9J8文档编码:CU8H5R6X9Q6 HV7R9M9V6J3 ZO6Z9A5Y9J8文档编码:CU8H5R6X9Q6 HV7R9M9V6J3 ZO6Z9A5Y9J8文档编码:CU8H5R6X9Q6 HV7R9M9V6J3 ZO6Z9A5Y9J8文档编码:CU8H5R6X9Q6 HV7R9M9V6J3 ZO6Z9A5Y9J8文档编码:CU8H5R6X9Q6 HV7R9M9V6J3 ZO6Z9A5Y9J8文档编码:CU8H5R6X9Q6 HV7R9M9V6J3 ZO6Z9A5Y9J8文档编码:CU8H5R6X9Q6 HV7R9M9V6J3 ZO6Z9A5Y9J8文档编码:CU8H5R6X9Q6 HV7R9M9V6J3 ZO6Z9A5Y9J8文档编码:CU8H5R6X9Q6 HV7R9M9V6J3 ZO6Z9A5Y9J8文档编码:CU8H5R6X9Q6 HV7R9M9V6J3 ZO6Z9A5Y9J8文档编码:CU8H5R6X9Q6 HV7R9M9V6J3 ZO6Z9A5Y9J8文档编码:CU8H5R6X9Q6 HV7R9M9V6J3 ZO6Z9A5Y9J8文档编码:CU8H5R6X9Q6 HV7R9M9V6J3 ZO6Z9A5Y9J8文档编码:CU8H5R6X9Q6 HV7R9M9V6J3 ZO6Z9A5Y9J8文档编码:CU8H5R6X9Q6 HV7R9M9V6J3 ZO6Z9A5Y9J8文档编码:CU8H5R6X9Q6 HV7R9M9V6J3 ZO6Z9A5Y9J8文档编码:CU8H5R6X9Q6 HV7R9M9V6J3 ZO6Z9A5Y9J8文档编码:CU8H5R6X9Q6 HV7R9M9V6J3 ZO6Z9A5Y9J8文档编码:CU8H5R6X9Q6 HV7R9M9V6J3 ZO6Z9A5Y9J8文档编码:CU8H5R6X9Q6 HV7R9M9V6J3 ZO6Z9A5Y9J8文档编码:CU8H5R6X9Q6 HV7R9M9V6J3 ZO6Z9A5Y9J8文档编码:CU8H5R6X9Q6 HV7R9M9V6J3 ZO6Z9A5Y9J8文档编码:CU8H5R6X9Q6 HV7R9M9V6J3 ZO6Z9A5Y9J8文档编码:CU8H5R6X9Q6 HV7R9M9V6J3 ZO6Z9A5Y9J8文档编码:CU8H5R6X9Q6 HV7R9M9V6J3 ZO6Z9A5Y9J8文档编码:CU8H5R6X9Q6 HV7R9M9V6J3 ZO6Z9A5Y9J8文档编码:CU8H5R6X9Q6 HV7R9M9V6J3 ZO6Z9A5Y9J8文档编码:CU8H5R6X9Q6 HV7R9M9V6J3 ZO6Z9A5Y9J8文档编码:CU8H5R6X9Q6 HV7R9M9V6J3 ZO6Z9A5Y9J8文档编码:CU8H5R6X9Q6 HV7R9M9V6J3 ZO6Z9A5Y9J8文档编码:CU8H5R6X9Q6 HV7R9M9V6J3 ZO6Z9A5Y9J8文档编码:CU8H5R6X9Q6 HV7R9M9V6J3 ZO6Z9A5Y9J8文档编码:CU8H5R6X9Q6 HV7R9M9V6J3 ZO6Z9A5Y9J8文档编码:CU8H5R6X9Q6 HV7R9M9V6J3 ZO6Z9A5Y9J8文档编码:CU8H5R6X9Q6 HV7R9M9V6J3 ZO6Z9A5Y9J8文档编码:CU8H5R6X9Q6 HV7R9M9V6J3 ZO6Z9A5Y9J8文档编码:CU8H5R6X9Q6 HV7R9M9V6J3 ZO6Z9A5Y9J8文档编码:CU8H5R6X9Q6 HV7R9M9V6J3 ZO6Z9A5Y9J8文档编码:CU8H5R6X9Q6 HV7R9M9V6J3 ZO6Z9A5Y9J8文档编码:CU8H5R6X9Q6 HV7R9M9V6J3 ZO6Z9A5Y9J8文档编码:CU8H5R6X9Q6 HV7R9M9V6J3 ZO6Z9A5Y9J8A1D1DC1CABB1符号表示：|ababa温馨提示：作用：判定或证明线面平行。关键：在平面内找或作出一条直线与面外的直线平行。思想：空间问题转化为平面问题三归纳形成定理先由学生口头总结，然后教师归纳总结 由多媒体幻灯片展示：1、线面平行的判定定理：平面外的一条直线与平面内的一条直线平行，则该直线与这个平面平行。2、定理的符号表示：|ababa简述：内外线线平行则线面平行3、定理运用的关键是找 作面内的线与面外的线平行，途径有：取中点利用平行四边形或三角形中位线性质等。【练 习 1】师 生 共 做 ：如 图，长 方 体ABCD A1B1C1D1中，与 AB 平行的平面是 _ 与 AA1平行的平面是 _ 与 AD 平行的平面是 _ 四应用定理，稳固与提高例 1：空间四边形相邻两边中点的连线，平行于经过另外两边的平面已知：空间四边形ABCD 中，E、F 分别是 AB、AD 的中点求证：EF平面 BCDA B C D E F 文档编码:CU8H5R6X9Q6 HV7R9M9V6J3 ZO6Z9A5Y9J8文档编码:CU8H5R6X9Q6 HV7R9M9V6J3 ZO6Z9A5Y9J8文档编码:CU8H5R6X9Q6 HV7R9M9V6J3 ZO6Z9A5Y9J8文档编码:CU8H5R6X9Q6 HV7R9M9V6J3 ZO6Z9A5Y9J8文档编码:CU8H5R6X9Q6 HV7R9M9V6J3 ZO6Z9A5Y9J8文档编码:CU8H5R6X9Q6 HV7R9M9V6J3 ZO6Z9A5Y9J8文档编码:CU8H5R6X9Q6 HV7R9M9V6J3 ZO6Z9A5Y9J8文档编码:CU8H5R6X9Q6 HV7R9M9V6J3 ZO6Z9A5Y9J8文档编码:CU8H5R6X9Q6 HV7R9M9V6J3 ZO6Z9A5Y9J8文档编码:CU8H5R6X9Q6 HV7R9M9V6J3 ZO6Z9A5Y9J8文档编码:CU8H5R6X9Q6 HV7R9M9V6J3 ZO6Z9A5Y9J8文档编码:CU8H5R6X9Q6 HV7R9M9V6J3 ZO6Z9A5Y9J8文档编码:CU8H5R6X9Q6 HV7R9M9V6J3 ZO6Z9A5Y9J8文档编码:CU8H5R6X9Q6 HV7R9M9V6J3 ZO6Z9A5Y9J8文档编码:CU8H5R6X9Q6 HV7R9M9V6J3 ZO6Z9A5Y9J8文档编码:CU8H5R6X9Q6 HV7R9M9V6J3 ZO6Z9A5Y9J8文档编码:CU8H5R6X9Q6 HV7R9M9V6J3 ZO6Z9A5Y9J8文档编码:CU8H5R6X9Q6 HV7R9M9V6J3 ZO6Z9A5Y9J8文档编码:CU8H5R6X9Q6 HV7R9M9V6J3 ZO6Z9A5Y9J8文档编码:CU8H5R6X9Q6 HV7R9M9V6J3 ZO6Z9A5Y9J8文档编码:CU8H5R6X9Q6 HV7R9M9V6J3 ZO6Z9A5Y9J8文档编码:CU8H5R6X9Q6 HV7R9M9V6J3 ZO6Z9A5Y9J8文档编码:CU8H5R6X9Q6 HV7R9M9V6J3 ZO6Z9A5Y9J8文档编码:CU8H5R6X9Q6 HV7R9M9V6J3 ZO6Z9A5Y9J8文档编码:CU8H5R6X9Q6 HV7R9M9V6J3 ZO6Z9A5Y9J8文档编码:CU8H5R6X9Q6 HV7R9M9V6J3 ZO6Z9A5Y9J8文档编码:CU8H5R6X9Q6 HV7R9M9V6J3 ZO6Z9A5Y9J8文档编码:CU8H5R6X9Q6 HV7R9M9V6J3 ZO6Z9A5Y9J8文档编码:CU8H5R6X9Q6 HV7R9M9V6J3 ZO6Z9A5Y9J8文档编码:CU8H5R6X9Q6 HV7R9M9V6J3 ZO6Z9A5Y9J8文档编码:CU8H5R6X9Q6 HV7R9M9V6J3 ZO6Z9A5Y9J8文档编码:CU8H5R6X9Q6 HV7R9M9V6J3 ZO6Z9A5Y9J8文档编码:CU8H5R6X9Q6 HV7R9M9V6J3 ZO6Z9A5Y9J8文档编码:CU8H5R6X9Q6 HV7R9M9V6J3 ZO6Z9A5Y9J8文档编码:CU8H5R6X9Q6 HV7R9M9V6J3 ZO6Z9A5Y9J8文档编码:CU8H5R6X9Q6 HV7R9M9V6J3 ZO6Z9A5Y9J8文档编码:CU8H5R6X9Q6 HV7R9M9V6J3 ZO6Z9A5Y9J8文档编码:CU8H5R6X9Q6 HV7R9M9V6J3 ZO6Z9A5Y9J8文档编码:CU8H5R6X9Q6 HV7R9M9V6J3 ZO6Z9A5Y9J8文档编码:CU8H5R6X9Q6 HV7R9M9V6J3 ZO6Z9A5Y9J8文档编码:CU8H5R6X9Q6 HV7R9M9V6J3 ZO6Z9A5Y9J8文档编码:CU8H5R6X9Q6 HV7R9M9V6J3 ZO6Z9A5Y9J8文档编码:CU8H5R6X9Q6 HV7R9M9V6J3 ZO6Z9A5Y9J8文档编码:CU8H5R6X9Q6 HV7R9M9V6J3 ZO6Z9A5Y9J8文档编码:CU8H5R6X9Q6 HV7R9M9V6J3 ZO6Z9A5Y9J8文档编码:CU8H5R6X9Q6 HV7R9M9V6J3 ZO6Z9A5Y9J8文档编码:CU8H5R6X9Q6 HV7R9M9V6J3 ZO6Z9A5Y9J8文档编码:CU8H5R6X9Q6 HV7R9M9V6J3 ZO6Z9A5Y9J81.分析：根据直线与平面平行的判定定理，要证明 EF平面 BCD，只要在平面 BCD 内找一直线与 EF平行即可，很明显原平面BCD 内的直线 BDEF生共做：证明：连结 BD性，这三个条件是证明直线和平面平行的条件，缺一不可变式(学生活动)：空间四边形 ABCD 中，E、F 分别是AB、AD 上的点，且 AE=31AB，AF=31AD 求证：EF平面 BCD小结：通过证明线线平行来证明线面平行，蕴含数学转化思想，关键在于找平行线，故又要用到中位线定理等；判定定理三个条件缺一不可。例 2 是平行四边形 ABCD 外一点同 M，N分别是PC，AB的中点。求证：MN/平面 PAD1.分析：取 PD 中点。:思考并书写证明过程。3.教师点评：指出可能的典型错误。A B C D E F DCABPNM文档编码:CU8H5R6X9Q6 HV7R9M9V6J3 ZO6Z9A5Y9J8文档编码:CU8H5R6X9Q6 HV7R9M9V6J3 ZO6Z9A5Y9J8文档编码:CU8H5R6X9Q6 HV7R9M9V6J3 ZO6Z9A5Y9J8文档编码:CU8H5R6X9Q6 HV7R9M9V6J3 ZO6Z9A5Y9J8文档编码:CU8H5R6X9Q6 HV7R9M9V6J3 ZO6Z9A5Y9J8文档编码:CU8H5R6X9Q6 HV7R9M9V6J3 ZO6Z9A5Y9J8文档编码:CU8H5R6X9Q6 HV7R9M9V6J3 ZO6Z9A5Y9J8文档编码:CU8H5R6X9Q6 HV7R9M9V6J3 ZO6Z9A5Y9J8文档编码:CU8H5R6X9Q6 HV7R9M9V6J3 ZO6Z9A5Y9J8文档编码:CU8H5R6X9Q6 HV7R9M9V6J3 ZO6Z9A5Y9J8文档编码:CU8H5R6X9Q6 HV7R9M9V6J3 ZO6Z9A5Y9J8文档编码:CU8H5R6X9Q6 HV7R9M9V6J3 ZO6Z9A5Y9J8文档编码:CU8H5R6X9Q6 HV7R9M9V6J3 ZO6Z9A5Y9J8文档编码:CU8H5R6X9Q6 HV7R9M9V6J3 ZO6Z9A5Y9J8文档编码:CU8H5R6X9Q6 HV7R9M9V6J3 ZO6Z9A5Y9J8文档编码:CU8H5R6X9Q6 HV7R9M9V6J3 ZO6Z9A5Y9J8文档编码:CU8H5R6X9Q6 HV7R9M9V6J3 ZO6Z9A5Y9J8文档编码:CU8H5R6X9Q6 HV7R9M9V6J3 ZO6Z9A5Y9J8文档编码:CU8H5R6X9Q6 HV7R9M9V6J3 ZO6Z9A5Y9J8文档编码:CU8H5R6X9Q6 HV7R9M9V6J3 ZO6Z9A5Y9J8文档编码:CU8H5R6X9Q6 HV7R9M9V6J3 ZO6Z9A5Y9J8文档编码:CU8H5R6X9Q6 HV7R9M9V6J3 ZO6Z9A5Y9J8文档编码:CU8H5R6X9Q6 HV7R9M9V6J3 ZO6Z9A5Y9J8文档编码:CU8H5R6X9Q6 HV7R9M9V6J3 ZO6Z9A5Y9J8文档编码:CU8H5R6X9Q6 HV7R9M9V6J3 ZO6Z9A5Y9J8文档编码:CU8H5R6X9Q6 HV7R9M9V6J3 ZO6Z9A5Y9J8文档编码:CU8H5R6X9Q6 HV7R9M9V6J3 ZO6Z9A5Y9J8文档编码:CU8H5R6X9Q6 HV7R9M9V6J3 ZO6Z9A5Y9J8文档编码:CU8H5R6X9Q6 HV7R9M9V6J3 ZO6Z9A5Y9J8文档编码:CU8H5R6X9Q6 HV7R9M9V6J3 ZO6Z9A5Y9J8文档编码:CU8H5R6X9Q6 HV7R9M9V6J3 ZO6Z9A5Y9J8文档编码:CU8H5R6X9Q6 HV7R9M9V6J3 ZO6Z9A5Y9J8文档编码:CU8H5R6X9Q6 HV7R9M9V6J3 ZO6Z9A5Y9J8文档编码:CU8H5R6X9Q6 HV7R9M9V6J3 ZO6Z9A5Y9J8文档编码:CU8H5R6X9Q6 HV7R9M9V6J3 ZO6Z9A5Y9J8文档编码:CU8H5R6X9Q6 HV7R9M9V6J3 ZO6Z9A5Y9J8文档编码:CU8H5R6X9Q6 HV7R9M9V6J3 ZO6Z9A5Y9J8文档编码:CU8H5R6X9Q6 HV7R9M9V6J3 ZO6Z9A5Y9J8文档编码:CU8H5R6X9Q6 HV7R9M9V6J3 ZO6Z9A5Y9J8文档编码:CU8H5R6X9Q6 HV7R9M9V6J3 ZO6Z9A5Y9J8文档编码:CU8H5R6X9Q6 HV7R9M9V6J3 ZO6Z9A5Y9J8文档编码:CU8H5R6X9Q6 HV7R9M9V6J3 ZO6Z9A5Y9J8文档编码:CU8H5R6X9Q6 HV7R9M9V6J3 ZO6Z9A5Y9J8文档编码:CU8H5R6X9Q6 HV7R9M9V6J3 ZO6Z9A5Y9J8文档编码:CU8H5R6X9Q6 HV7R9M9V6J3 ZO6Z9A5Y9J8文档编码:CU8H5R6X9Q6 HV7R9M9V6J3 ZO6Z9A5Y9J8文档编码:CU8H5R6X9Q6 HV7R9M9V6J3 ZO6Z9A5Y9J8文档编码:CU8H5R6X9Q6 HV7R9M9V6J3 ZO6Z9A5Y9J8【练习 2】独立完成，再交流 正方体 ABCD A1B1C1D1中，有为DD1的中点，试判断 BD1与平面 AEC 的位置关系，并说明理由。五课堂活动探索思考题：如图，正方体 ABCD-A1B1C1 D1中，E、F 分别是棱 BC、C1D1上的中点.求证：EF平面 BB1D1D.学生利用学习小组讨论、交流；教师分组指导；总结、交流。A B C D F E A1B1C1D1C1D1A1B1CBADE文档编码:CU8H5R6X9Q6 HV7R9M9V6J3 ZO6Z9A5Y9J8文档编码:CU8H5R6X9Q6 HV7R9M9V6J3 ZO6Z9A5Y9J8文档编码:CU8H5R6X9Q6 HV7R9M9V6J3 ZO6Z9A5Y9J8文档编码:CU8H5R6X9Q6 HV7R9M9V6J3 ZO6Z9A5Y9J8文档编码:CU8H5R6X9Q6 HV7R9M9V6J3 ZO6Z9A5Y9J8文档编码:CU8H5R6X9Q6 HV7R9M9V6J3 ZO6Z9A5Y9J8文档编码:CU8H5R6X9Q6 HV7R9M9V6J3 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ZO6Z9A5Y9J8文档编码:CU8H5R6X9Q6 HV7R9M9V6J3 ZO6Z9A5Y9J8文档编码:CU8H5R6X9Q6 HV7R9M9V6J3 ZO6Z9A5Y9J8文档编码:CU8H5R6X9Q6 HV7R9M9V6J3 ZO6Z9A5Y9J8文档编码:CU8H5R6X9Q6 HV7R9M9V6J3 ZO6Z9A5Y9J8文档编码:CU8H5R6X9Q6 HV7R9M9V6J3 ZO6Z9A5Y9J8文档编码:CU8H5R6X9Q6 HV7R9M9V6J3 ZO6Z9A5Y9J8文档编码:CU8H5R6X9Q6 HV7R9M9V6J3 ZO6Z9A5Y9J8文档编码:CU8H5R6X9Q6 HV7R9M9V6J3 ZO6Z9A5Y9J8文档编码:CU8H5R6X9Q6 HV7R9M9V6J3 ZO6Z9A5Y9J8文档编码:CU8H5R6X9Q6 HV7R9M9V6J3 ZO6Z9A5Y9J8文档编码:CU8H5R6X9Q6 HV7R9M9V6J3 ZO6Z9A5Y9J8文档编码:CU8H5R6X9Q6 HV7R9M9V6J3 ZO6Z9A5Y9J8文档编码:CU8H5R6X9Q6 HV7R9M9V6J3 ZO6Z9A5Y9J8文档编码:CU8H5R6X9Q6 HV7R9M9V6J3 ZO6Z9A5Y9J8文档编码:CU8H5R6X9Q6 HV7R9M9V6J3 ZO6Z9A5Y9J8文档编码:CU8H5R6X9Q6 HV7R9M9V6J3 ZO6Z9A5Y9J8六归纳整理1、同学们在运用该判定定理时应注意什么？2、在解决空间几何问题时，常将之转换为平面几何问题。七作业布置 直线与平面平行的判定B28 题单八板书设计九教学反思电脑演示屏直线与平面平行的判定线线平行线面平行例题 1 例题 2 1、定义法2、判定定理文档编码:CU8H5R6X9Q6 HV7R9M9V6J3 ZO6Z9A5Y9J8文档编码:CU8H5R6X9Q6 HV7R9M9V6J3 ZO6Z9A5Y9J8文档编码:CU8H5R6X9Q6 HV7R9M9V6J3 ZO6Z9A5Y9J8文档编码:CU8H5R6X9Q6 HV7R9M9V6J3 ZO6Z9A5Y9J8文档编码:CU8H5R6X9Q6 HV7R9M9V6J3 ZO6Z9A5Y9J8文档编码:CU8H5R6X9Q6 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