1、1 1、二面角及二面角的平面角、二面角及二面角的平面角的有关定义的有关定义平面的一条直线把平面分为平面的一条直线把平面分为两两部分，部分，其中的每一部分都叫做一个其中的每一部分都叫做一个半平面半平面。从一条从一条直线出发的两个半平面所直线出发的两个半平面所组成的图形叫做组成的图形叫做二面角二面角。（1 1）半平面半平面（2 2）二面角二面角l lll这条直线叫做二面角的棱棱，每个半平面叫做二面角的面面。BOAa（4）二面角的记法“面面1 1棱棱面面2 2”如：以直线a为棱，以、为半平面的二面角记作：以直线AB为棱，平面CAB、平面DAB为半平面的二面角记作：等等。以直线l为棱，以平面ABCD、
2、平面A1B1C1D1为半平面的二面角记作：或“AlA1”，等等。？“a a”？“面ABCDl面A1B1C1D1”？“CABD”(3)常见二面角的画法B。OA(5)(5)二面角的平面角二面角的平面角垂直于二面角的棱的任一平面与两个半平面的交线所成的角叫做二面角的平面角。或：从二面角的棱上任一点在两个半平面内分别作垂直于棱的射线，则这两条射线所成的角叫做二面角的平面角。B。OAB1。O1A1B。OA小结：小结：B。OA复习回顾复习回顾等角定理等角定理 若一个角的两边与若一个角的两边与另一个角的两边分别平行且方另一个角的两边分别平行且方向相同，则这两个角相等。向相同，则这两个角相等。1.二面角就是用
3、它的平面角来度量的。一个二面角的平面角多大，我们就说个二面角是多少度的二面角。2.二面角的平面角与点（或垂直平面）的位置无任何关系，只与二面角的张角大小有关。(6)二面角的范围00。,180,180。（7）直二面角平面角为直角的二面角叫做直二面角当堂小测1、二面角指的是（）A、从一条直线出发的两个半平面所夹的角度。B、从一条直线出发的两个半平面所组成的图形。C、两个平面相交时，两个平面所夹的锐角。D、过棱上一点和棱垂直的二射线所成的角。2、二面角的平面角的顶点在二面角的上，角的两边分别在二面角的内，且两边都与棱，它的度数与它的平面角的度数。2.课堂诊断例1 在60。的二面角的棱上有两个点A、B
4、，AC、BD分 别在二面角的两个面内且垂直于AB，已知AB=4cm，AC=6cm，BD=8cm，求CD的长。CDAB分析分析要要求求CD的的长长，可可考考虑虑用用向向量量法法，即即求求|CD|，要要求求|CD|，须须先先用用已已知知向向量量CA、AB、BD 表表示示它它，不不难难得得到到：CD=CA+AB+BD 最最后后根根据据|a|2=aa 求求出出结结果果.3.有关二面角的题型解解：由由已已知知得得：CA，BD18060120，CAAB0，ABBD0|CD|2（CAABBD）2|CA|2|AB|2|BD|22CABD|CA|2|AB|2|BD|22|CA|BD|cosCA，BD 62428
5、2268cos120 6242822682168|CD|217 例 2、如图所示，在正方体 AC1中，求二面角 A1BDC1的大小。解：（方 法 一）由 正 方 体 的 面 对 角 线 长 都 相 等 可 知，A1B D与 C1B D 是 全 等 的 正 三 角 形，取B D 的 中 点O，连 结A1O、C1O，则A1O B D，C1O B D，A1O C 就 是 二 面 角A1 B D C1的 平 面 角。A1C12a，A1O C1O 232a 26a c o s A1O C aaaaa26262)2()26()26(22231 A1O C a rc c o s31。故 二 面 角A1 B
6、D C1的 大 小 为a rc c o s31。D(0，0，0)，B(1，1，0)，O(21，21，0)，A1(1，0，1)，C1(0，1，1)BD(0，0，0)(1，1，0)（1，1，0）1OA(1，0，1)(21，21，0)（21，21，1）1OC(0，1，1)(21，21，0)（21，21，1）解：（方法二）如图建立空间直角坐标系，设正方体的棱长为 1，BD 的中点为 O，则 BD1OA121（1）（21）010 BD1OC（1）（21）121010 1OA1OC21（21）（21）211121 1OA1OC26 OA1BD，OC1BD，1OA，1OC就是二面角 A1BDC1的平面角。c
7、os1OA，1OC|1111OCOAOCOA 26262131。例3、如图，设E、F、G是正方体相应棱的中点，求二面角EFGA的大小。H解：如图，过点A作AH交CF的延长线于点H，连结EH。由EA平面AC及三垂线三垂线定理可得：在RtEAH中，易得 AH22EF，EFEA，tanEHA2，EHAarctan2。EH FG，故EHA就是二面角 EFGA的平面角。1、二面角的定义2、二面角的平面角的定义3、二面角的平面角的求解：找（或作）出平面角定义法棱的垂面法三垂线定理法向量法等求解解三角形或用向量的夹角公式作业布置 课本第47页4、5（3）作业初一英语第二学期同步串讲初一英语第二学期同步串讲
8、第七讲第七讲 Do you have an eraser?Do you have a soccer ball?soccer basketballbadmintonbaseballball gamestennis(racket)volleyballgolfPing pong(ball)table tennis Do you have an American football/rugby?Yes,I do./No,I dont.Golf clubDo you have a golf ball?Yes,I do./No,I dont.Group workNames Do you have a?Bal
9、ls you haveLucyYes,I do.basketballWhat balls do you have?I have.1.你有一个排球吗？你有一个排球吗？是的，我有。是的，我有。2.你有表兄妹吗你有表兄妹吗?不不,我没有。我没有。3.她有网球拍吗？她有网球拍吗？是的，她有。是的，她有。7.咱们去踢球吧。咱们去踢球吧。Do you have a volleyball?Yes,I do.Do you have any cousins?No,I dont.Does she have a tennis racket?Yes,she does.Lets play soccer.4.他有英英字典
10、吗？他有英英字典吗？不，他没有。他有一不，他没有。他有一本英汉字典。本英汉字典。5.他们有笔记本吗？他们有笔记本吗？是的，他们有。是的，他们有。6.让我看一看。让我看一看。Does he have an English English dictionary?No,he doesnt.He has an English Chinese dictionary?Do they have any note books?Yes,they do.Lets have a look.Does he have a tennis racket?Yes,he does./No,he doesnt.Does she
11、have a soccer ball?Yes,she does./No,she doesnt.Does he have a basketball?Yes,he does.Do they have a puck?Yes,they do./No,they dont.ice hockeyA:I want to play baseball.Do you have a baseball bat?B:No,I dont.A:Does your brother have one?B:Yes,he does.Lets go and find him.Lets play volleyball.That soun
12、ds good.Lets play barbell.BarbellThat sounds boring.Lets play bowling.That sounds interesting.Lets play baseball.That sounds difficult.Lets go skateboarding.That sounds fun.(exciting)Lets play Ping Pong.That sounds relaxing.let sb.do sth.Lets have a break.Lets go and play Ping-pong.Our School Sports
13、 Center needs new members.Fill in the enrollment form if you want to join the clubs.First name _ Last name _Age _ Sex _Class _ Club _Reason _Whats your first name,please?How old are you?What class are you in?What club do you want to join?Why?(Because I like)写出反义词写出反义词 dislike_ interesting _ good_ we
14、ll_ easy_ lost _ day _ different _ big _ first _ on _ in front of _ this _ these _ bring _ Fill in the blanks1.A:Excuse me,_ you _ a baseball?B:No,I _.A:_ Jim _ one?B:Yes,he _.Lets go and find him.2.A:Hi,Sally.B:Hi,Jane.A:Sally,_ _ my friend,Lucy.B:Hi,Lucy._ to meet you.C:Nice to _ you,_.do havedont
15、Does havedoesthis is Nice meet too A:Lets play volleyball.B:That _ interesting,but I _ have one.A:Well,_ you have a tennis bat?B:Yes,I _.Lets go and play tennis.A:Thats a good _.soundsdontdodoidea1.Does B have an eraser?2.Is the shop open?3.What day is today?4.What can they do?No,she doesnt.No,it is
16、nt.It is closed.Today is Friday.They go to the supermarket.Part 11.What would B like?2.How much money does B have?3.Where is her purse?4.What does she do?She only has two yuan.Her purse is at home.She borrows four yuan from C.Part 2Shed like a red pencil and a pencil-sharpener.1.Does Jim have a dict
17、ionary?2.Does Ann have a dictionary?3.Who has an English-Chinese dictionary?4.When can Li Lei give it back?Part 3No,he doesnt.Lucy has one.He can give it back next Monday.No,she doesnt.close *closed 1.The shop closes at 8 pm.2.Please close the door.3.The door is closed.4.The shop is closed.5.The sho
18、p is open.borrow from 1.I borrow a book from him.2.May I borrow a pen from you?3.Dont borrow money from her.May I 1.May I come in?2.May I borrow a pen from you?3.May I sit down?give back (to sb.)1.Please give the money back tomorrow.2.I can give the book back to him next week.3.Can you give my dicti
19、onary back this afternoon?There is something wrong with1.There is something wrong with my TV/his pen/your computer.2.There is something wrong with him/her/you/the boy.3.Whats wrong with you?4.Whats wrong with your TV?close *closed borrow from May I give back (to sb.)There is something wrong withYou
20、are going to have a P.E class,think about some activities.Talk about them.Time _ Place _ Sport _ Reason _Writing Write a passage about yourself and your friend.What sports do you play?What sports things do you have?What other things do you do?What about your friend?(parent)Key points:Key points:Food
21、 Do you like bananas?Does he/she like bananas?Do you like bananas?Do you like bananas?Do you like oranges?Yes,I do.No,I dont.Does he like apples?Yes,he does.No,he doesnt.Does she like peaches?Yes,she does.No,she doesnt.Do they like grapes?Yes,they do.No,they dont.I like hamburgers for breakfast.But
22、I dont like eggs.Do your parents Do your parents like pizza?like pizza?Yes,they do.Yes,they do.No,they dont.No,they dont.Does your father Does your father like beer?like beer?Yes,he does.Yes,he does.No,he doesnt.No,he doesnt.Choose the right words.1.There are five _(tomatoes,tomato)on the table.2.Th
23、e _(child,children)are in the room.3.She _(doesnt like,dont like)chicken for lunch.4.He _(likes,like)hamburgers.5.Do they_(likes,like)apples?6.Mike doesnt like_(bananas,banana).7.My mother doesnt have _(a lunch,lunch)at home.8.Does she _(like,likes)French fries?用所给动词的适当形式填空。1.She _(not like)salad.2.
24、_you _(like)oranges?3.He _(eat)lots of healthy food every day.4.There _(be)some chicken on the plate.5.His mother_(like)ice cream.6._your father _(like)eggs for breakfast?7.They_(not like)playing tennis.8.There_(be)some potatoes in the bag.9.My mother_(have)supper at home every day.10.Mr.Green_(not
25、have)lunch at school every day.A:Do you want to go to a movie?B:Yes,I do.That sounds good.A:What kind of movies do you like?B:I like action movies because they are exciting.And I think cartoons are interesting.A:How about thrillers?B:No.Thrillers are scary.How about you?A:I dont like thrillers,either.But I like documentaries.I think theyre instructive.Does he want to go to a movie?Yes,he does./No,he doesnt.What kind of movies does he want to see?He wants to see a comedy.What do you like to do on holidays?Why do you like?
