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新人教版高中英语必修2Unit 4 History and traditions教案
这个地区有着深厚的传统。既学既练：为了让更多的外国游客了解中国文化，欣赏中国美丽的自然风光，感受中国发生的巨大变化，某外文杂志社将出版一本英语小册子来介绍中国的旅游景点。该杂志社邀请你为该小册子写一篇英语短文来介绍杭州，内容包括：1．杭州的位置(中国东南部)、面积(16 000多平方公里)及历史(2 200多年)等；2．杭州的旅游特色(自然风景、传统文化、特色小吃等)；3．希望更多的游客来杭州参观。注意：1．词数80左右；2．可适当增加细节，以使行文连贯。Located in the southeast of China, Hangzhou is a beautiful city．Dating back more than 2，200 years, Hangzhou covers an area of more than 16，000 square kilometers．In Hangzhou, you can visit the West Lake, whose scenery is fascinating．In addition, you can’t miss its cultural relics and historical sites, from which you will learn more about excellent Chinese traditional culture and traditions．In Hangzhou, the special snacks are famous and visitors from different parts of the world think highly of them．As a tourist attraction, Hangzhou attracts a large number of visitors from home and abroad every year．Once you come to China, Hangzhou is a scenic spot you can’t miss．
新人教版高中英语必修2Unit 5 Music-Listening＆Speaking＆Talking教案
choir memberspeople to run food stands people to sell festival ticketspeople to sell music CDspeople to set up equipmentmusical performersStep 2: Listen to the announcement again and answer the questions. ? 1. What kind of songs will Grace Davis sing at the festival?? 2. Who can try out as a performer?? 3. What can those who think they do not have musical talent do?? 4. How can students volunteer to take part?? Talking about preferences:? Would you prefer doing ..?? What would you prefer to do?? Would you rather do .... or ….?? What would you rather do?? I'd prefer .... to ..? I'd rather have ... than .. Step 3: Speaking ProjectWork in groups. Role-play the conversation or make a new one.? Debbie: Where have you been? You missed the announcement about the music festival.? John: I was at the doctor's office. Music festival?? Frank: Yes, it's going to be next month on the school sports field. John, you can play the piano. How about playing it at the festival?? John: Well, I'd rather play the violin. I can play Liang Zhu.? Frank: Wow! Sounds good. What about you, Debbie? ? Debbie: Actually, I don't have much musical ability. I'd prefer just to help out with the crowds.? Frank: You can sell tickets or work at a food stand.? John: So can I assume that the aim of the festival is to raise money?? Debbie: Yes. All of the money will go to charity.
新人教版高中英语必修2Unit 5 Music-Discovering Useful Structures教案一
Step1:自主探究。1．(教材P52)Born(bear) in the USA on 2 January 1970, Whitacre began studying music at the University of Nevada in 1988．2．(教材P52) Moved(move) by this music, he said, “It was like seeing color for the first time．”3．(教材P56)I was very afraid and I felt so alone and discouraged(discourage)．4．(教材P58)Encouraged(encourage) by this first performance and the positive reaction of the audience, I have continued to play the piano and enjoy it more every day．Step2:语法要点精析。用法1：过去分词作表语1）．过去分词可放在连系动词be, get, feel, remain, seem, look, become等之后作表语，表示主语所处的状态Tom was astonished to see a snake moving across the floor．汤姆很惊讶地看到一条蛇正爬过地板。Finally the baby felt tired of playing with those toys．终于婴儿厌倦了玩那些玩具。注意：1）.过去分词作表语时与被动语态的区别过去分词作表语时，强调主语所处的状态；而动词的被动语态表示主语是动作的承受者，强调动作。The library is now closed．(状态)图书馆现在关闭了。The cup was broken by my little sister yesterday．(动作)昨天我妹妹把杯子打碎了。2）感觉类及物动词的现在分词与过去分词作表语的区别过去分词作表语多表示人自身的感受或事物自身的状态，常译作“感到……的”；现在分词多表示事物具有的特性，常译作“令人……的”。
新人教版高中英语必修2Unit 5 Music-Listening and Speaking教案
This lesson is about music. Students can classify the types of music through the instruments and its sound and can talk about their preferences about music, even join some activities and play a role in them according to their musical talents. On the basis, they are guided to use the languages to express their preferences and some plosive sounds and their rules.1. Classify the music types through the instruments and its sound.2. Listen and understand what the speakers’ preferences are and the reasons; talk about their own preferences and give their own reasons, using these sentences: “What kind of music do you like? And why? “ “Because it makes/gives me energy/peaceful.../touches my heart...”.3. Learn some plosives and the rules.4. Join some activities and play a role in them according to the talents. 1. Listen and understand what the speakers’ preferences are and the reasons;2. talk about their own preferences and give their own reasons, using these sentences: “What kind of music do you like? And why? “ “Because it makes/gives me energy/peaceful.../touches my heart...”.3. Learn some plosives and incomplete plosives and its rules.Step 1 Lead inPoint at the pictures on P50 and ask Q1: What are the people doing in the pictures below?Q2: What kind of music they are?Then play the MP3s one by oneStep 2 ListeningTask 1: A reporter from the school newspaper is interviewing students about music. Listen to the interviews. Draw lines between the words to make complete sentences. Some words will not be used.
新人教版高中英语必修2Unit 5 Music-Reading and Thinking教案一
This section focuses on "learning about experiencing music Online". This virtual choir is a new form of music performance. Members from all over the world don't need to love to come to a place. Instead, they use the new technology to model the various parts and wonderful virtual harmony group of music in the family. Students need to understand the main meaning of each paragraph. Finding topic sentences is an important way to understand the general idea of a paragraph. After the topic sentence, it is usually the detail sentence that supports and explains the topic sentence. Some paragraphs have obvious subject sentences, for example, the first sentence of the second paragraph is the subject sentence of the paragraph, and the following sentenceStudents need to pay attention to the topic sentences and key sentences, and then pay attention to how the sentences after the meaning explain, explain and support the topic sentences or key sentences before.1.Guide students to learn about experiencing music online2.Guide students to scan and circle the information in the text.3.Guide students to find the numbers and dates to fill in the timeline.4.Guide students to learn more about music by completing the sentences with the correct forms of the words and phrases. And then make a mind map about the outline of the passage.1. Guide students to pay attention to reading strategies, such as prediction, self-questioning and scanning.2. Help students sort out the main meaning of each paragraph and understand the narrative characteristics of "timeline” in illustrative style.3. Lead students to understand the changes that have been caused by the Internet.
新人教版高中英语必修2Unit 5 Music-Reading For Writing教案一
(4)Now we have heard a number of outstanding speeches ... 我们已经聆听了许多精彩的发言……(5)Because we wanted the nations of the world, working together, to deal with ... 因为我们希望全世界各国团结起来去应对……(6)And if we do not act ... 如果我们不采取行动……(7)Now, I share the concerns that have been expressed ... 我也同意对于……表达的担心(8)Let us show the world that by working together we can ... 让我们告诉全世界，通过一起努力我们可以……(9)It is now time for us to ... 是时候我们……(10)And I have always wished that ... 我一直希望……(11)Thank you for letting me share this day with me.感谢你们和我共度这一天。实践演练：假如你是高中生李华，你校将举办一次以“音乐”为主题的演讲比赛，请你按照主题，写下你的演讲稿。注意：词数100左右。First of all, thank you for listening to my speech. My topic is: love music like love yourself.Music is like the air we need to maintain our normal lives around us. You can't imagine how terrible a world without music would be. Movies and TV shows have no music, only dry conversations and scenes; mobile phones only vibrations; streets only noisy crowds; cafes, western restaurants only depressed meals. What a terrible world it is!As a student, I hope we all can enjoy the fun brought by music in our spare time. Instead of just listening to music, we can even make our own music. Let's enjoy the fun of music!Thanks again for your attention!
新人教版高中英语选修1Unit 1 People of Achievement教案
【设计意图】 基于上述分析，学生总结新闻故事语篇类型的特征，即标题的省略性、导语的概括性、数据的支撑性和引语的重要性。在此过程中，学生对新闻故事语篇类型有了更深层次的了解，对于学生阅读和写作具有重要意义。Activity 7: Discussing to make a writing outline.本活动为实现课时目标3。1.Discuss and make an outline.Ask students to discuss in groups of four and make their own writing outline.To celebrate the 70th anniversary of the People’s Republic of China, our school newspaper starts a new column about “People of Achievement”. You plan to write a news story about one of the winners of the Medal of the Republic in 2019, including Yu Min, Shen Jilan, Sun Jiadong, Li Yannian, Zhang Fuqing, Yuan Longping, Huang Xuhua and Tu Youyou.【设计意图】 教师创设情境，即为庆祝新中国成立70周年，校报新增有关卓有成就人物的栏目，你将从共和国勋章获得者中，选择一位写一篇新闻故事，向该栏目投稿。学生以小组合作形式，展开讨论，并写出新闻故事框架，有助于学生课后收集人物信息，撰写新闻故事。
新人教版高中英语选修1Unit 2 Looking into the Future教案
【设计意图】以“新科技是一把双刃剑”为主题开展讨论活动。这个话题比较大，所以给了一定的限制，首先需要以智能家居为例来阐述科技发展对未来生活产生的影响，然后列举其优点和缺点，最后就以上现象发表自己的观点。这个活动是对整个文本的创意性总结与意义的升华，留给学生一定的想象空间，学生借此机会可以运用文本内容和语言表达自己对科技发展的看法和态度。Assignments:1. Finish Exercise 4 on Page 15 of the textbook.A smart home is one that integrated computers into the structure of the building itself. In this way, many of the things that we now do ourselves become automatic. For example, the smart home could control the air conditioning and lights so that you would no longer have to turn switches on and off, and so that your home would be more energy-efficient. The smart home could also monitor itself to make sure that everything is working as it should, and send you warnings if there is a problem. Such smart homes could even be programmed to detect your health problems, and then give you reasonable advice as to the food you should eat or if you should see a doctor. So, in a sense, smart homes will lead us to living smarter lives.2.Create a smart function for your home, and share your creation in the next period.
新人教版高中英语选修1Unit 4 Body Language教案
本阅读材料的话题是交际中的肢体语言，作者从三个方面讲述了肢体语言的特征与作用，通过主题句和举例阐述的方式让读者了解不同文化中肢体语言的相同或者不同的意义，并从更抽象、概括的维度深入认识肢体语言的特点，理解肢体语言的作用。基于肢体语言的特点，作者提醒读者在与人交流中，尤其是当文化背景有差异的时候，要使用得体的肢体语言，尊重、理解和包容不同的文化，进行有效、有素养的沟通。文本共由六个段落组成，篇章结构为“总—分”。第一段用简练的语言引出了话题，并且从我们自身表达的需要和了解他人感受两个角度讲述了肢体语言的作用。第二段阐述了肢体语言的第一个重要特点——肢体语言在不同的文化中有不同的内涵——这也是文中写作篇幅最大的一个要点，最为重要。通过讲述肢体语言的这一特点，作者向读者传递了要尊重不同的文化、要使用与所在文化相宜的肢体语言。
新人教版高中英语选修1Unit 5 Working the Land教案
1. 完成文本主要信息填空（斜体字部分设空）：As a witness to farmers’ poor harvests and even a severe shortage of food, Yuan Longping was determined to devote his life to tackling this crisis. After graduation, he realized that what farmers needed most was to boost yields in the fields. Yuan was convinced that the answer lay in the creation of hybrid rice, one characteristic of which is that it usually achieve higher output than conventional crops. However, it was no easy job. The first difficulty he needed to overcome was scientists’ general assumption that this could not be done. Through trial and error, Yuan managed to generate this incredible crop. It is estimated that about 60 percent of domestic rice consumption in China was comprised of crops generated from Yuan’s hybrid strains. His innovation has enabled Chinese farmers to considerably expand their output and helped feed the world. Unwilling to retire early to a life of leisure and unconcerned about celebrity or fortune, Yuan continues to turn one vision after another into realities.2. 模仿写作：Do some research via the Internet and introduce another agricultural scientist, Chen Risheng（陈日胜）, using the structure, expressions and writing techniques you have learnt from the text “A Pioneer for All People”.【设计意图】任务1是对文本内容和词汇学习成效的检测。任务2借助文本中学到的词汇和写作手法仿写另一位科学家，提升学生迁移运用词汇、文体结构和写作方法的能力。
新人教版高中英语选修4Unit 2 Iconic Attractions教案
帮助学生通过讨论与对主题的提升，反思自己的旅游方式，以便做出更优化的安排，在今后的旅程中有更多的收益。 Activity 2: Further discussion of the 6 elements above and supplement of more background knowledge 本活动为实现课时教学目标2。 1.Target Q: The writer’s clear target of traveling, meeting the people and experiencing the culture, is closely related to his major in social studies. Then what is social studies? Social studies is a part of a school or college curriculum concerned with the study of social relationships and the functioning of society and usually made up of courses in history, government, economics, civics, sociology, geography, and anthropology. （Dictionary by Merriam-Webster） Reflection: When you go out to travel, what targets do you usually have in mind? 2.Research Q: Suppose you are traveling to Hangzhou during the school holidays, how will you do research on the city? (surf the internet, read books or travel brochures, consult friends, ...) What information will you be interested to know? (location, iconic sites, local cuisines, interesting customs, shopping malls ...) 3.Abandonment To make the most of time, we have to learn to abandon so that we can accomplish our plan. What will you be interested in doing if you go to Hangzhou if you have a week’s time? What if you only have 2 days? 4~5. Venturing & Experiencing Q: What did he venture to do during the trip? What new experiences did he have? In Sydney: attend his first open-air barbecue, enjoy many different but yummy meals In Catherine: observe the life and customs of the aborigines appreciate their music & try the musical instruments: the didgeridoo
新人教版高中英语选修4Unit 4 Sharing教案
【核心素养提升点】学会将抽象信息进行可视化表达，提高信息处理能力和分析、推理等高阶思维品质；在跨文化交际中学会以国际视野接受和包容不同的文化。 5.Read Paragraph 2, draw a mind map and answer the questions. Q1:What did Jo learn about Tombe’s life? Q2:What kind of life do the natives lead? Read paragraph 2-5 and draw a mind-map. (Focus on accommodation, possession, diet and belief) 【设计意图】引导学生利用思维导图和问题链等形式来厘清当地人的生活方式，更好地处理和归纳信息 【核心素养提升点】提高信息处理能力、分析和归纳能力，包容异国文化、扩展国际视野。 6.Read Paragraph 3 and answer the questions. Q1:What was Jo’s feeling upon arriving her own home? Q2:Why would she feel that way? Q3:Do you think “It was such a privilege to have spent a day with Tombe’s family”? 【设计意图】通过提问，让学生理解Jo的苦并快乐的心情，并通过对“It was such a privilege to have spent a day with Tombe’s family”这句话的理解，体验志愿者生活的伟大。 【核心素养提升点】学会对信息的综合和归纳，从而理解作者所表达的观点。 Activity4: Summarize the change of Jo's feelings
新人教版高中英语选修4Unit 5 Language Your Career教案
本单元阅读文本向中学生推荐职业能力测试(Career Aptitude Test)，旨在建议学生利用职业倾向测试来发现自己更感兴趣、更有潜力的学习或职业方向，并规划自己的未来职业。 本文采用了建议性文本，全篇从职业生涯的重要意义讲起，针对中学生对职业规划比较迷茫的现状，提出了职业倾向测试这一建议。全文共七段，其中第一段和第二段为第一部分，其余五段为第二部分。第一部分论述职业的重要性和职业生涯规划的最佳时间是在校期间，第二部分提出解决职业选择困惑可以通过完成职业能力测试，介绍了不同种类的职业倾向测试，结合图表详细说明其中一种操作步骤，并提醒职业建议也基于学历和经验，最后一段概括论述，建议学生通过职业能力测试这一有效的工具，找到自己真正热爱的事物。 在文本教学设计时，要帮助学生梳理有关职业的话题语言。阅读策略层面，指导学生通过学习图表和图形，在有限的空间内获取广泛信息，如阅读图表标题，图表上的标签，X轴Y轴上的数据所指。
四年级下册综合实践活动教学计划及教案
一、教材分析 1、教材内容及所处地位综合实践活动是在新一轮基础教育课程改革中应运而生的新型课程。所谓综合实践活动，主要指以学生的兴趣和直接经验为基础，以与学生学习生活和社会生活密切相关的各类现实性、综合性、实践性问题为内容，以研究性学习为主导学习方式，以培养学生的创新精神、实践能力及体现对知识的综合运用为主要目的一类新型课程。具有以下特点： 1、基于兴趣与直接经验。2、回归生活世界。3、立足实践。4、着眼创新。5、以研究性学习为主导学习方式：（1）以转变学生的学习方式为出发点。（2）强调知识的联系和综合运用。（3）注重过程。（4）强调开放。（5）重视师生互动。四年级下册综合实践活动课程要培养学生对生活、学习的积极态度，使他们具备一定的交往合作能力、观察分析能力、动手操作能力；要让他们初步掌握参与社会实践的方法，信息资料的搜集、分析和处理问题的方法以及研究探索的方法；使学生形成合作、分享、积极进取等良好的个性品质，成为创新生活的小主人。2、单元内容分析本教材包括?方法与指导?和?活动与探究?两部分内容， ?方法与探究? 主要是让学生掌握如何进行采访，通过一系列活动，掌握采访的准备、注意事项、具体实施，及最后的交流总结，培养学生交往能力。 ?活动与探究?包括六个主题，主题一我们身边的标志，通过让学生认识标志，体会含义。学会分类，最后学会制作标志，循序渐进，蕴含了创新、守规、审美等能力的培养；主题二早餐与健康通过谈论，调查、分析讨论培养学生交流总结能力，树立健康生活意识；主题三，有趣的丝网花，通过制作培养学生合作、审美、动手能力；主题四巧手做风筝继续对学生进行培养;主题五植物的扦插与嫁接，与现实生活联系密切，通过活动掌握方法，体验快乐，体验劳动的乐趣；主题六争做小小志愿者，通过了解体验志愿者的活动，丰富阅历，培养学生的服务意识，自身获得提升与发展。教材的重点、难点：重点：学会交流，提升能力；认识各种标志，学会制作；学会健康的生活；通过制作丝网花、风筝、植物的扦插于嫁接，学会制作，提高动手能力，通过体验小小志愿者，提高服务意识。难点：教学中让学生亲身参与、主动实践，在实践中综合运用所学知识解决各种实际问题，提高解决实际问题的能力。学习基础：四年级学生已具备了一定的实践能力，因此要逐步培养学生一些探究问题的方法，提高学生的动手意识，能够从生活和学习中挖掘自己感兴趣的活动主题，能够试着和同学展开小组合作学习，在有效的活动中不断提高学生的动手与创新的潜能。
北师大初中九年级数学下册正切与坡度1教案
已知一水坝的横断面是梯形ABCD，下底BC长14m，斜坡AB的坡度为3∶3，另一腰CD与下底的夹角为45°，且长为46m，求它的上底的长(精确到0.1m，参考数据：2≈1.414，3≈1.732)．解析：过点A作AE⊥BC于E，过点D作DF⊥BC于F，根据已知条件求出AE＝DF的值，再根据坡度求出BE，最后根据EF＝BC－BE－FC求出AD.解：过点A作AE⊥BC，过点D作DF⊥BC，垂足分别为E、F.∵CD与BC的夹角为45°，∴∠DCF＝45°，∴∠CDF＝45°.∵CD＝46m，∴DF＝CF＝462＝43(m)，∴AE＝DF＝43m.∵斜坡AB的坡度为3∶3，∴tan∠ABE＝AEBE＝33＝3，∴BE＝4m.∵BC＝14m，∴EF＝BC－BE－CF＝14－4－43＝10－43(m)．∵AD＝EF，∴AD＝10－43≈3.1(m)．所以，它的上底的长约为3.1m.方法总结：考查对坡度的理解及梯形的性质的掌握情况．解决问题的关键是添加辅助线构造直角三角形．
北师大初中九年级数学下册垂径定理教案
方法总结：垂径定理虽是圆的知识，但也不是孤立的，它常和三角形等知识综合来解决问题，我们一定要把知识融会贯通，在解决问题时才能得心应手．变式训练：见《学练优》本课时练习“课后巩固提升”第2题【类型三】 动点问题如图，⊙O的直径为10cm，弦AB＝8cm，P是弦AB上的一个动点，求OP的长度范围．解析：当点P处于弦AB的端点时，OP最长，此时OP为半径的长；当OP⊥AB时，OP最短，利用垂径定理及勾股定理可求得此时OP的长．解：作直径MN⊥弦AB，交AB于点D，由垂径定理，得AD＝DB＝12AB＝4cm.又∵⊙O的直径为10cm，连接OA，∴OA＝5cm.在Rt△AOD中，由勾股定理，得OD＝OA2－AD2＝3cm.∵垂线段最短，半径最长，∴OP的长度范围是3cm≤OP≤5cm.方法总结：解题的关键是明确OP最长、最短时的情况，灵活利用垂径定理求解．容易出错的地方是不能确定最值时的情况．
北师大初中九年级数学下册第一章复习教案
一、本章知识要点： 1、锐角三角函数的概念； 2、解直角三角形。二、本章教材分析： （一）.使学生正确理解和掌握三角函数的定义，才能正确理解和掌握直角三角形中边与角的相互关系，进而才能利用直角三角形的边与角的相互关系去解直角三角形，因此三角形函数定义既是本章的重点又是理解本章知识的关键,而且也是本章知识的难点。如何解决这一关键问题，教材采取了以下的教学步骤：1. 从实际中提出问题，如修建扬水站的实例，这一实例可归结为已知RtΔ的一个锐角和斜边求已知角的对边的问题。显然用勾股定理和直角三角形两个锐角互余中的边与边或角与角的关系无法解出了，因此需要进一步来研究直角三角形中边与角的相互关系。2. 教材又采取了从特殊到一般的研究方法利用学生的旧知识，以含30°、45°的直角三角形为例：揭示了直角三角形中一个锐角确定为30°时，那么这角的对边与斜边之比就确定比值为1：2。
北师大初中九年级数学下册切线长定理教案
(3)若要满足结论，则∠BFO＝∠GFC，根据切线长定理得∠BFO＝∠EFO，从而得到这三个角应是60°，然后结合已知的正方形的边长，也是圆的直径，利用30°的直角三角形的知识进行计算．解：(1)FB＝FE，PE＝PA；(2)四边形CDPF的周长为FC＋CD＋DP＋PE＋EF＝FC＋CD＋DP＋PA＋BF＝BF＋FC＋CD＋DP＋PA＝BC＋CD＋DA＝23×3＝63；(3)假设存在点P，使BF·FG＝CF·OF.∴BFOF＝CFFG.∵cos∠OFB＝BFOF，cos∠GFC＝CFFG，∴∠OFB＝∠GFC.∵∠OFB＝∠OFE，∴∠OFE＝∠OFB＝∠GFC＝60°，∴在Rt△OFB中，BF＝OBtan∠OFB＝OBtan60°＝1.在Rt△GFC中，∵CG＝CF·tan∠GFC＝CF·tan60°＝(23－1)×3＝6－3，∴DG＝CG－CD＝6－33，∴DP＝DG·tan∠PGD＝DG·tan30°＝23－3，∴AP＝AD－DP＝23－(23－3)＝3.方法总结：由于存在性问题的结论有两种可能，所以具有开放的特征，在假设存在性以后进行的推理或计算．一般思路是：假设存在——推理论证——得出结论．若能导出合理的结果，就做出“存在”的判断，若导出矛盾，就做出“不存在”的判断．
北师大初中九年级数学下册圆教案
解析：首先求得圆的半径长，然后求得P、Q、R到Q′的距离，即可作出判断．解：⊙O′的半径是r＝ 12＋12＝2，PO′＝2＞2，则点P在⊙O′的外部；QO′＝1＜2，则点Q在⊙O′的内部；RO′＝（2－1）2＋（2－1）2＝2＝圆的半径，故点R在圆上．方法总结：注意运用平面内两点之间的距离公式，设平面内任意两点的坐标分别为A(x1，y1)，B(x2，y2)，则AB＝（x1－x2）2＋（y1－y2）2.【类型四】 点与圆的位置关系的实际应用如图，城市A的正北方向50千米的B处，有一无线电信号发射塔．已知，该发射塔发射的无线电信号的有效半径为100千米，AC是一条直达C城的公路，从A城发往C城的客车车速为60千米/时．(1)当客车从A城出发开往C城时，某人立即打开无线电收音机，客车行驶了0.5小时的时候，接收信号最强．此时，客车到发射塔的距离是多少千米(离发射塔越近，信号越强)?(2)客车从A城到C城共行驶2小时，请你判断到C城后还能接收到信号吗？请说明理由．
北师大初中九年级数学下册圆的对称性教案
我们知道圆是一个旋转对称图形，无论绕圆心旋转多少度，它都能与自身重合，对称中心即为其圆心．将图中的扇形AOB(阴影部分)绕点O逆时针旋转某个角度，画出旋转之后的图形，比较前后两个图形，你能发现什么？二、合作探究探究点：圆心角、弧、弦之间的关系【类型一】 利用圆心角、弧、弦之间的关系证明线段相等如图，M为⊙O上一点，MA︵＝MB︵，MD⊥OA于D，ME⊥OB于E，求证：MD＝ME.解析：连接MO，根据等弧对等圆心角，则∠MOD＝∠MOE，再由角平分线的性质，得出MD＝ME.证明：连接MO，∵ MA︵＝MB︵，∴∠MOD＝∠MOE，又∵MD⊥OA于D，ME⊥OB于E，∴MD＝ME.方法总结：圆心角、弧、弦之间相等关系的定理可以用来证明线段相等．本题考查了等弧对等圆心角，以及角平分线的性质．
