1、二面角 从空间一直线出发的两个半从空间一直线出发的两个半一一、二面角的定义二面角的定义二二、二面角的平面角二面角的平面角角角 的平面角的平面角 一个平面垂直于二面角一个平面垂直于二面角的棱，并与两半平的棱，并与两半平面分别相交于射线面分别相交于射线PA、PB垂足为垂足为P，则，则APB叫做二面叫做二面ABP平面所组成的图形叫做二面角平面所组成的图形叫做二面角1、定义、定义二面角二面角2、作二面角的平面角的常用方法、作二面角的平面角的常用方法、点、点P在棱上在棱上、点、点P在一个半平面上在一个半平面上、点、点P在二面角内在二面角内pABABpABOp定义法定义法三垂线定理法三垂线定理法垂面法垂面
2、法二面角1、如图，、如图，AB是圆的直径，是圆的直径，PA垂垂直圆所在的平面，直圆所在的平面，C是圆上任一是圆上任一点，则二面角点，则二面角P-BC-A的平面角为的平面角为:A.ABP B.ACP C.都不是都不是 练练 习习2、已知、已知P为二面角为二面角 内一内一点，且点，且P到两个半平面的距离都等到两个半平面的距离都等于于P到棱的距离的一半，则这个二到棱的距离的一半，则这个二面角的度数是多少？面角的度数是多少？pABOABCP60二面角例例1.1.如图，已知如图，已知P P是二面角是二面角-ABAB-棱上一点，过棱上一点，过P P分分别 在别 在 、内 引 射 线内 引 射 线P MP
3、M、P NP N，且，且 M P N=6 0 M P N=6 0 BPM=BPN=45BPM=BPN=45 ，求此二面角的度数。，求此二面角的度数。ABPMNCDO解解：在PB上取不同于P 的一点O，在内过O作OCAB交PM于C，在内作ODAB交PN于D，连CD，可得COD是二面角-AB-的平面角设PO=a，BPM=BPN=45CO=a，DO=a，PC a，PD a22又MPN=60 CD=PC a2COD=90因此，二面角的度数为因此，二面角的度数为90aOPC二面角例例2 2如图如图P P为二面角为二面角 内一点，内一点，PA,PBPA,PB,且且PA=5PA=5，PB=8PB=8，AB=
4、7AB=7，求这二面角的度数。，求这二面角的度数。过过PA、PB的平面的平面PAB与与 棱棱 交于交于O点点PA PA PB PB 平面PABAOB为二面角的平面角又PA=5，PB=8，AB=721cosP由余弦定理得由余弦定理得P=60 AOB=120 这二面角的度数为这二面角的度数为120解：解：ABPO二面角OABPC取取AB 的中点为的中点为E，连连PE，OEO为为 AC 中点中点，ABC=90OEBC且且 OE BC212221在RtPOE中，OE ，PO 22tanPEO22所求的二面角所求的二面角P-AB-C 的正切值为的正切值为例例3 3如图，三棱锥如图，三棱锥P-ABCP-A
5、BC的顶点的顶点P P在底面在底面ABCABC上的射影上的射影是底面是底面RtRtABCABC斜边斜边ACAC的中点的中点O O，若，若PB=AB=1PB=AB=1，BC=BC=，求二面角，求二面角P-AB-CP-AB-C的正切值的正切值。2PEO为二面角为二面角P-AB-C 的平面角的平面角23在在RtPBE中中，BE ，PB=1，PE21OEAB，因此因此 PEABE解：解：EOP二面角练习练习1 1：已知已知RtRtABCABC在平面在平面 内，斜边内，斜边ABAB在在3030的二的二面角面角-AB-AB-的棱的棱上，若上，若AC=5AC=5，BC=12BC=12，求点，求点C C到平到
6、平面面的距离的距离CO。ACBOD练习练习2 2：在平面四边形：在平面四边形ABCDABCD中，中，AB=BC=2AB=BC=2，AD=CD=,B=120AD=CD=,B=120；将三角形；将三角形ABCABC沿四边形沿四边形ABCDABCD的对角线的对角线ACAC折起来，使折起来，使DB=DB=，求，求AB CAB C所所在平面与在平面与ADCADC所在平面所成二面角的平面角的度数。所在平面所成二面角的平面角的度数。157ABCBDO二面角二二、二面角的平面角二面角的平面角一一、二面角的定义二面角的定义 从空间一直线出发的两个半平面所组成的图形叫做二面角1、定义、定义2、求二面角的平面角方法
7、、求二面角的平面角方法点点P在棱上在棱上点点P在一个半平面上在一个半平面上点点P在二面角内在二面角内ABP小小结结ABppABpABO定义法定义法三垂线定理法三垂线定理法垂面法垂面法二面角ABCD A A为二面角为二面角 CD CD 的棱的棱CDCD上上一点，一点，ABAB在平面在平面 内且与棱内且与棱CDCD成成4545角，又角，又ABAB与平面与平面成成30，求二，求二面角面角 CD CD 的大小。的大小。作作业业二面角二面角初一英语第二学期同步串讲初一英语第二学期同步串讲 第七讲第七讲 Do you have an eraser?Do you have a soccer ball?soc
8、cer 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?Balls you haveLucyYes,I do.basketballWhat balls do you have?I
9、 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？
10、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 have a soccer ball?Yes,she does./No,she doesnt.Does he hav
11、e 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 sounds good.Lets play barbell.BarbellThat sounds boring.Lets p
12、lay 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 Center needs new members.Fill in the enrollment form if y
13、ou 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_ well_ easy_ lost _ day _ different _ big _ first _ on _ in f
14、ront 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 havedontDoes havedoesthis isNice meet too A:Lets play volleyball.B
15、: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 isnt.It is closed.Today is Friday.They go to the supermarket.
16、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 dictionary?2.Does Ann have a dictionary?3.Who has an English-Ch
17、inese 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 shop is open.borrow from 1.I borrow a book from him.2.May I bo
18、rrow 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 dictionary back this afternoon?There is something wrong with1.Th
19、ere 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 are going to have a P.E class,think about some activities.T
20、alk 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 Do you like bananas?Does he/she like bananas?Do you like b
21、ananas?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 I dont like eggs.Do your parents Do your parents like pizza
22、?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.The _(child,children)are in the room.3.She _(doesnt like,dont
23、 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._you _(like)oranges?3.He _(eat)lots of healthy food every d
24、ay.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 have)lunch at school every day.A:Do you want to go to a mov
25、ie?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?
