图书馆警示语英语

合集下载

英语警示语大全60条

英语警示语大全60条1. Caution: Wet floor!2. Danger: High voltage.3. Warning: No trespassing.4. Please wear protective gear.5. Caution: Steep stairs ahead.6. Danger: Do not climb.7. Warning: Slippery surface.8. Keep out: Authorized personnel only.9. Caution: Sharp objects.10. Danger: Beware of falling debris.11. Warning: Flammable materials.12. Caution: Hot surface.13. Danger: E某plosive contents.14. Warning: To某ic chemicals.15. Please handle with care.16. Caution: Falling rocks.17. Danger: Do not enter.18. Warning: Fire hazard.19. Caution: Automatic door.20. Danger: Watch your step.21. Warning: Wet paint.22. Please do not touch.23. Caution: Low clearance.24. Danger: Do not touch high voltage wires.25. Warning: Harmful radiation.26. Caution: Slippery when wet.27. Danger: Keep out of reach of children.28. Warning: Biohazard.29. Please do not smoke.30. Caution: Fragile items.31. Danger: Do not disturb.32. Warning: Do not open.33. Caution: Flammable liquids.34. Danger: Do not operate without proper training.35. Warning: Use caution when working with machinery.36. Please dispose of trash properly.37. Caution: Falling objects.38. Danger: Stay away from edges.39. Warning: Do not overload.40. Caution: High noise levels.41. Danger: Do not enter without permission.42. Warning: E某iting vehicles only.43. Please fasten seatbelts.44. Caution: Slippery when icy.45. Danger: Do not swim in unauthorized areas.46. Warning: Keep away from open flames.47. Caution: Electrical shock.48. Danger: Keep hands clear.49. Warning: Do not operate machinery with loose clothing.50. Please keep off the grass.51. Caution: Hazardous materials.52. Danger: Do not operate while into某icated.53. Warning: Do not use cell phones while driving.54. Please do not feed the animals.55. Caution: Uneven pavement.56. Danger: Do not lean over railing.57. Warning: Do not run on stairs.58. Caution: Do not touch moving parts.59. Danger: Do not enter confined spaces without proper ventilation.60. Warning: Do not leave valuables unattended.。

哈弗图书馆励志标语中英文

哈佛大学图书馆馆训1.此刻打盹，你将做梦；而此刻学习，你将圆梦。

T h i s m o m e n t w i l l n a p,y o u w i l l h a v e a d r e a m;b u t t h i s m o m e n t s t u d y,y o u w i l l i n t e r p r e t ad re a m.2.我荒废的今日，正是昨日殒身之人祈求的明日。

I l e a v e u n c u l t i v a t e d t o d a y,w a s p r e c i s e l y y e s t e r d a y p e r i s h e s t o m o r r o w w h i c h p e r s o n o f t h eb o d y i m p l o r e d.3.觉得为时已晚的时候，恰恰是最早的时候。

T h o u g h t i s a l r e a d y i s l a t e,e x a c t l y i s t h e e a r l i e s t t i m e.4.勿将今日之事拖到明日。

N o t m a t t e r o f t h e t o d a y w i l l d r a g t o m o r r o w.5.学习时的苦痛是暂时的，未学到的痛苦是终生的。

T i m e t h e s t u d y p a i n i s t e m p o r a r y,h a s n o t l e a r n e d t h e p a i n i s l i f e-l o n g.6.学习这件事，不是缺乏时间，而是缺乏努力。

S t u d i e s t h i s m a t t e r,l a c k s t h e t i m e,b u t i s l a c k s d i l i g e n t l y.7.幸福或许不排名次，但成功必排名次。

公共场合警示语英文大全

公共场合警示语英文大全English:
1. "No smoking"
2. "Do not litter, keep the environment clean"
3. "Wash your hands before leaving the restroom"
4. "No unauthorized personnel beyond this point"
5. "Please keep noise to a minimum"
6. "Mind the gap"
7. "Beware of pickpockets"
8. "Caution: wet floor"
9. "For your safety, do not lean on the doors"
10. "No loitering or soliciting"
中文翻译:
1. "禁止吸烟"
2. "不要乱丢垃圾，保持环境清洁"
3. "离开洗手间前请洗手"
4. "未经许可人员不得进入此地点"
5. "请保持噪音最小限度"
6. "注意缝隙"
7. "小心扒手"
8. "注意：地板湿滑"
9. "为了您的安全，请勿靠近门"
10. "禁止逗留或招揽"。

小学英语作文图书馆标语

小学英语作文图书馆标语Libraries are the heart and soul of any educational institution, serving as a hub of knowledge, exploration, and intellectual growth. For elementary school students, the library can be a magical place, where they can embark on thrilling adventures through the pages of books, discover new worlds, and cultivate a lifelong love of learning. As such, it is crucial to craft a captivating library slogan that not only captures the essence of the library's purpose but also inspires and engages young minds.One powerful slogan that could resonate with elementary school students is "Unlock the Treasure Trove of Knowledge." This phrase conveys the idea that the library is a veritable treasure trove, brimming with a vast array of knowledge and resources waiting to be discovered. The use of the word "unlock" suggests that the library holds the key to unlocking these treasures, beckoning students to venture forth and explore.Another compelling slogan could be "Explore, Discover, Grow: Your Gateway to Adventure." This slogan emphasizes the library as agateway to adventure, where students can embark on exciting journeys of exploration and discovery. The phrase "Explore, Discover, Grow" captures the multifaceted nature of the library experience, where students can not only explore new ideas and concepts but also discover their own passions and interests, ultimately fostering their personal growth and development.A third option for a library slogan could be "Imagine, Innovate, Inspire: The Library Ignites the Spark of Creativity." This slogan highlights the library's role in igniting the spark of creativity within young minds. By encouraging students to imagine, innovate, and inspire, the library becomes a hub of creative expression, where students can explore their artistic and intellectual talents, and be inspired to think outside the box.Regardless of the specific slogan chosen, it is essential that the message resonates with the target audience – the elementary school students. The slogan should be concise, memorable, and reflective of the library's core values and objectives. It should also be visually appealing, with a design that complements the overall branding and aesthetic of the school.One way to ensure the effectiveness of the library slogan is to involve the students in the creative process. By soliciting ideas and input from the students themselves, the resulting slogan is morelikely to resonate with the target audience and foster a sense of ownership and investment in the library's identity.Furthermore, the library slogan should be prominently displayed throughout the school, serving as a constant reminder of the library's significance and the opportunities it presents. This could be achieved through the use of posters, banners, or even digital displays, ensuring that the slogan is constantly visible and accessible to the students.Beyond the slogan, it is crucial to create a welcoming and engaging library environment that aligns with the message conveyed. This could involve creating designated reading nooks, interactive displays, or even hosting regular events and activities that encourage students to explore and discover the treasures within the library.By crafting a captivating library slogan and fostering a dynamic and inviting library environment, elementary schools can cultivate a love of reading and learning in their students. This, in turn, can lead to improved academic performance, enhanced critical thinking skills, and the development of well-rounded individuals who are equipped to navigate the challenges of the 21st century.In conclusion, the library slogan for an elementary school should be a reflection of the institution's commitment to fostering intellectualcuriosity, creativity, and a lifelong love of learning. Whether it's "Unlock the Treasure Trove of Knowledge," "Explore, Discover, Grow: Your Gateway to Adventure," or "Imagine, Innovate, Inspire: The Library Ignites the Spark of Creativity," the chosen slogan should inspire and engage the young minds of the school community, guiding them on a journey of discovery and growth.。

英语公共场所提示语

英语公共场所提示语第一篇：英语公共场所提示语公共场所常见提示用语Useful Phrases in Public Places Keep Silence肃静 Smoking Prohibied严禁吸烟 Spitting Forbidden严禁吐痰No Admittance不许入内Closed 此门不通Knock 请先敲门Push 请向前推Push请向后拉Queue up for Bus 排队上车Admittance free免费入场 Admission by Ticket Only 凭票入场 Seat by number对号入座Closed during Repairs 儿童谢绝入场Inspections Declined 谢绝参观 Closed during Repairs修理店面，暂停营业Times’s Over下班时间 Road up, Detour 马路翻修，车辆绕行Danger Ahead 前面危险Commit No Nuisance禁止小便Cameras Forbidden严禁拍照No Overtaking禁止超车Slow(or Drive Slow)车辆慢行Keep Off the Grass勿踏草地 Shooting Prohibited 严禁打猎第二篇：学校公共场所提示语学校公共场所提示语警示破坏环境卫生者:爱护自己,就象爱护自己的家园一样;请爱护着优美的环境,因为我们在此生存.警示跨栏杆者:切勿翻越,痛苦就躲在那边恭候您;我并非不可逾越,但您的安危就在这一举之间.警示衣冠不整者:自身的形象是无言的诉说,衣冠整洁是您的自尊,社会文明需要您去装点.用与卫生间者:自己方便,更要予人方便,我把方便留给您,您把方便留给大家.用于果皮箱:我藏污纳垢是为了您生活得更美,请您别对我们存在视而不见,丢点什么时请您想一想,千万不要丢脸.花坛文明标语：绿草茵茵，踏之可惜。

草木成荫多好看，乱扔垃圾是添乱。

图书馆的英文警示语

哈佛大学图书馆馆训1.此刻打盹，你将做梦；而此刻学习，你将圆梦。

this moment will nap, you will have a dream; but this moment study, you will interpret a dream.2. 我荒废的今日，正是昨日殒身之人祈求的明日。

i leave uncultivated today, was precisely yesterday perishes tomorrow which person of the body implored.3. 觉得为时已晚的时候，恰恰是最早的时候。

thought is already is late, exactly is the earliest time.4. 勿将今日之事拖到明日。

not matter of the today will drag tomorrow.5. 学习时的苦痛是暂时的，未学到的痛苦是终生的。

time the study pain is temporary, has not learned the pain is life-long.6. 学习这件事，不是缺乏时间，而是缺乏努力。

studies this matter, lacks the time, but is lacks diligently.7. 幸福或许不排名次，但成功必排名次。

perhaps happiness does not arrange the position, but succeeds must arrange the position.8. 学习并不是人生的全部。

但，既然连人生的一部分——学习也无法征服，还能做什么呢？9. 请享受无法回避的痛苦。

please enjoy the pain which is unable to avoid.10. 只有比别人更早、更勤奋地努力，才能尝到成功的滋味。

公共场所的英文警示语图书馆的警示语英文

竭诚为您提供优质的服务，优质的文档，谢谢阅读/双击去除公共场所的英文警示语图书馆的警示语英文Atthistimethereisnosoundwinssound。

你们听说图书馆的警示语英文有哪些吗?那么小编为大家整理了图书馆的警示语英文，欢迎阅览!图书馆的警示语英文(热门)1.buildingaharmoniousworldofknowledge,readingachievementswonderfullife2.Quietatmospheretocreateawarmenvironment,silentmed itationgivesyouinfinitewisdom.catedisyourright,lovethebooksupportingbookisyo urduty.4.yougentlycome,justasyougentlyleave,andbeneficiala ndharmless5.gentlyIgo,asIgentlycome,donottakeabook6.handlewithcare,takecareofthebooks7.Lightneedleinadvertently,landingsound,thegentlema nintentionally,silentandnotlanguage8.pleasegiveothersaquietspace9.Timethestudypainistemporary,hasnotlearnedthepaini slifelong10.Thebookisamagicweaponofself-cultivation,isthepil larofthehumanspirit.11.Notjustromanticeloquencewins,silenttasteisthelongest.12.staticknowledge,maintenanceoneveryone13.Nomercytohismercy.14.booksaretheladderofhumanprogress15.statictoself-cultivation,learntomoraleducation 图书馆的标语英文(集锦)1.taticknowledge,maintenancebyeveryone2.readtenthousandbooks,travelingthousandsofmiles.3.confessionsofthebook:IhopethateventhoughIhavewrin kles,experiencedthevicissitudesoflife,youstilltakem easatreasureinthepalmofyourhand4.bookscanmakeupforignoranceandignorance5.Takeawaytheknowledge,leavingbehindcivilization6.Thecivilizationofchinaismorepowerful,thecivilized societyismoreharmonious,thecivilizedcampusismorebea utiful,thecivilizedlibraryismoreprecious7.Thebrightclassroomismyhome,spaciousandclean8.handlewithcare,takecareofthebooks.9.booksaretheeverburninglampsofaccumulatedwisdom10.booksarefriendsofhumanbeings11.booksaretheladderofhumanprogress12.booksarethebestnutritionalsupplementforpeople'ss piritualhunger13.Agoodbookisthebestoffriends,todayandtomorrow.14.createawarmandcomfortableenvironment,experiencea differentromanticlife15.Asoundmorequiet,likethousandsofknowledgetocreate abetterenvironment.16.yougoquietly,asquietlyasyoucame17.silencehasbeenraisedhereasavirtue18.Atthistimethereisnosoundwinssound19.eyeeartakesamomentalone.Atalltimesandinallcountr ies.20.Knowledgeisthecrystallizationofpreciousstones,cu ltureisthelusterofthegem图书馆的温馨警示语英文(最新)1.onlyreadingwithoutthinking,theconsequencesareconf used;onlythinkingnotreading,theconsequencesaredange rous2.cametotheseaintheheart,afraidofhurt3.Intheeyes,staticintheheart4.politenessisrightnexttoyou,pleasereadit5.booksareourgoodteachersandhelpfulfriends6.booksaregoodmedicinetohealthesoul7.Thismomentwillnap,youwillhaveadreambutthismoments tudy,youwillinterpretadream.8.statictoself-cultivation,learntomoraleducation.9.seekdevelopmentinharmony10.Thestaticcharacterishigh,Knowledgepark.11.booksarefriendsofhumanbeings,lovebooksistocarefo rfriends12.booksarethesourceofwisdom,readingistheladderofpr ogress13.studiesthismatter,lacksthetime,butislacksdiligen tly14.Thatis,toborrowbooks,returnbooks,backandforthord erly,everyonehappy15.readingmakesafoolwise,andwisemanwise 看过“图书馆的警示语英文”的人还看了：1.有创意的图书馆警示语2.有趣的图书馆的警示语3.关于图书室的警示语4.图书馆警示语怎么写5.图书馆创意的警示语最后，小编希望文章对您有所帮助，如果有不周到的地方请多谅解，更多相关的文章正在创作中，希望您定期关注。

图书馆须知英语作文

图书馆须知英语作文英文回答：Library Guidelines.1. Silence is essential. Please be respectful of others who are studying or working. Refrain from talking, laughing, or engaging in any other disruptive behavior.2. Keep the library clean. Please dispose of your trash properly and return books to their designated shelves. Food and drinks are not permitted in the library.3. Respect library property. Do not mark, fold, or tear pages of books or magazines. Report any damage to library staff immediately.4. Be considerate of others. Allow others to use the computers and study tables without interruption. Share resources and collaborate with others in a respectfulmanner.5. Follow all library regulations. Please be aware of the library's hours of operation, borrowing policies, and other rules and regulations.6. Ask for help. If you need assistance, please do not hesitate to ask a librarian. We are here to help you find resources, navigate the library, and answer your questions.7. Be responsible. Respect the library's resources and facilities. Use equipment carefully and report any problems to library staff.8. Report lost or stolen items. If you lose or steal an item, please report it to library staff immediately.9. Enjoy the library! The library is a place for learning, discovery, and community. We encourage you to make use of its resources and engage with the library community.中文回答：图书馆须知。

告知别人图书馆规则的英语作文

告知别人图书馆规则的英语作文英文回答：Library Rules.Libraries are essential institutions for education, research, and leisure. To ensure a productive and enjoyable experience for all patrons, it is important to adhere to the following library rules:1. Be quiet and respectful.The library is a shared space, and it is important to be mindful of others who are trying to study or read. This means keeping your voice down, avoiding loud conversations, and turning off your cell phone.2. Handle library materials with care.Books, magazines, and other library materials arevaluable resources that should be treated with respect. Always handle them carefully and avoid writing, marking, or tearing them. If you need to photocopy or scan an item, please ask a staff member for assistance.3. Return materials on time.All materials must be returned to the library by the due date. Overdue items will incur fines, and you may be unable to check out additional materials until the overdue items are returned.4. Be aware of the library's hours of operation.The library has specific hours of operation, and it is important to be aware of them so that you can plan your visits accordingly. The hours of operation may vary depending on the day of the week and the time of year.5. Follow the dress code.Some libraries have a dress code that must be followedby all patrons. This may include requirements for modest clothing, covering your shoes, or wearing a hat. Please be sure to check the library's website or ask a staff member for more information about the dress code.6. Be respectful of all library staff.The library staff is there to help you find the resources you need and to answer your questions. Please be polite and respectful to them, and do not hesitate to ask for assistance if you need it.7. Report any problems to the library staff.If you see any problems in the library, such as noise, vandalism, or theft, please report it to the library staff immediately. They will take appropriate action to address the problem.By following these library rules, you can help to create a positive and productive environment for everyone who uses the library.中文回答：图书馆规则。

图书馆不能干什么万能句型英语作文

人教版数学八年级上册全册全套试卷（Word版含解析）一、八年级数学三角形填空题（难）1．小明在用计算器计算一个多边形的内角和时，得出的结果为2005°，小芳立即判断他的结构是错误的，小明仔细地复算了一遍，果然发现自己把一个角的度数输入了两遍.你认为正确的内角和应该是________．【答案】1980【解析】【详解】解：设多边形的边数为n，多加的角度为α，则（n-2）×180°=2005°-α，当n=13时，α=25°，此时（13-2）×180°=1980°，α=25°故答案为1980．2．等腰三角形一边长是10cm，一边长是6cm，则它的周长是_____cm或_____cm．【答案】22cm,26cm【解析】【分析】题目给出等腰三角形有两条边长为10cm和6cm，而没有明确腰、底分别是多少，所以要进行讨论，还要应用三角形的三边关系验证能否组成三角形．【详解】（1）当腰是6cm时，周长＝6+6+10＝22cm；（2）当腰长为10cm时，周长＝10+10+6＝26cm，所以其周长是22cm或26cm．故答案为：22，26．【点睛】本题考查了等腰三角形的性质和三角形的三边关系；已知没有明确腰和底边的题目一定要想到两种情况，分类进行讨论，还应验证各种情况是否能构成三角形进行解答，这点非常重要，也是解题的关键．3．已知a，b，c是△ABC的三边长，a，b满足|a﹣7|+（b﹣1）2=0，c为奇数，则c=_____．【答案】7【解析】【分析】根据非负数的性质列式求出a、b的值，再根据三角形的任意两边之和大于第三边，两边之差小于第三边求出c的取值范围，再根据c是奇数求出c的值．【详解】∵a ，b 满足|a ﹣7|+（b ﹣1）2=0，∴a ﹣7=0，b ﹣1=0，解得a=7，b=1，∵7﹣1=6，7+1=8，∴68c <<，又∵c 为奇数，∴c=7，故答案为7．【点睛】本题考查非负数的性质：偶次方，解题的关键是明确题意，明确三角形三边的关系．4．如图，△ABC 中，∠A = 40°，∠B = 72°，CE 平分∠ACB ，CD ⊥AB 于D ，DF ⊥CE ，则∠CDF =_________度.【答案】74°【解析】【分析】【详解】试题分析：首先根据三角形的内角和定理求得∠ACB 的度数，以及∠BCD 的度数，根据角平分线的定义求得∠BCE 的度数，则∠ECD 可以求解，然后在△CDF 中，利用内角和定理即可求得∠CDF 的度数．∵∠A=40°，∠B=70°， ∴∠ACB=180°﹣∠A ﹣∠B=70°． ∵CE 平分∠ACB ，∴∠ACE=12∠ACB=35°． ∵CD ⊥AB 于D ， ∴∠CDA=90°， ∠ACD=180°﹣∠A ﹣∠CDA=50°．∴∠ECD=∠ACD ﹣∠ACE=15°． ∵DF ⊥CE ， ∴∠CFD=90°， ∴∠CDF=180°﹣∠CFD ﹣∠DCF=75°．考点：三角形内角和定理．5．如图，△ABC 中，∠B 与∠C 的平分线交于点O ，过O 作EF ∥BC 交AB 、AC 于E 、F ，若△ABC 的周长比△AEF 的周长大12cm ，O 到AB 的距离为4cm ，△OBC 的面积_____cm 2．【答案】242cm．【解析】【分析】由BE=EO可证得EF∥BC，从而可得∠FOC=∠OCF，即得OF=CF；可知△AEF等于AB+AC，所以根据题中的条件可得出BC及O到BC的距离，从而能求出△OBC的面积．【详解】∵BE=EO，∴∠EBO=∠EOB=∠OBC，∴EF∥BC，∴∠FOC=∠OCB=∠OCF，∴OF=CF；△AEF等于AB+AC，又∵△ABC的周长比△AEF的周长大12cm，∴可得BC=12cm，根据角平分线的性质可得O到BC的距离为4cm，∴S△OBC=12×12×4=24cm2．考点：1．三角形的面积；2．三角形三边关系．6．如图，△ABC中，∠BAC＝70°，∠ABC的平分线与∠ACB的外角平分线交于点O，则∠BOC＝_____度．【答案】35【解析】【分析】根据三角形的一个外角等于与它不相邻的两个内角的和可得∠BAC+∠ABC＝∠ACE，∠BOC+∠OBC＝∠OCE，再根据角平分线的定义可得∠OBC＝12∠ABC，∠OCE＝1 2∠ACE，然后整理可得∠BOC＝12∠BAC．【详解】解：由三角形的外角性质，∠BAC+∠ABC＝∠ACE，∠BOC+∠OBC＝∠OCE，∵∠ABC的平分线与∠ACB的外角平分线交于点O，∴∠OBC＝12∠ABC，∠OCE＝12∠ACE，∴12（∠BAC+∠ABC）＝∠BOC+12∠ABC，∴∠BOC＝12∠BAC，∵∠BAC＝70°，∴∠BOC＝35°，故答案为：35°．【点睛】本题考查了三角形的内角和定理、三角形的外角性质，掌握三角形的一个外角等于与它不相邻的两个内角的和的性质，要注意整体思想的利用．二、八年级数学三角形选择题（难）7．若△ABC内有一个点P1，当P1、A、B、C没有任何三点在同一直线上时，如图1，可构成3个互不重叠的小三角形；若△ABC内有两个点P1、P2，其它条件不变，如图2，可构成5个互不重叠的小三角形：……若△ABC内有n个点，其它条件不变，则构成若干个互不重叠的小三角形，这些小三角形的内角和为（）A．n·180°B．（n+2）·180°C．（2n-1）·180°D．（2n+1）·180°【答案】D【解析】【分析】当△ABC内的点的个数是1时，三角形内互不重叠的小三角形的个数是3；当△ABC内的点的个数是2时，三角形内互不重叠的小三角形的个数是5；依此类推得到当△ABC内的点的个数是3时，三角形内互不重叠的小三角形的个数是7；当△ABC内的点的个数是n 时，三角形内互不重叠的小三角形的个数2n+1，所以这些小三角形的内角和为（2n+1）·180°【详解】】解：图1中，当△ABC内只有1个点时，可分割成3个互不重叠的小三角形；图2中，当△ABC内只有2个点时，可分割成5个互不重叠的小三角形；图3中，当△ABC内只有3个点时，可分割成7个互不重叠的小三角形；根据以上规律，当△ABC内有n个点（P1，P2，…，P n）时，可以把△ABC分割成S=2n+1个互不重叠的三角形，所以这些小三角形的内角和为（2n+1）·180°.【点睛】此题考查了平面图形的有规律变化，要求学生通过观察图形，分析、归纳并发现其中的规律，并应用规律解决问题是解题的关键．8．如图，把一张长方形纸条ABCD 沿EF 折叠，C 、D 两点落到'C 、'D 处.已知20DAC ∠=，且''//C D AC ，则AEF ∠的度数为( )A ．20B ．35C ．50D ．70【答案】B【解析】【分析】依据C'D'//AC ，即可得到∠AHG=∠C′=90°，进而得出AGH 70∠=，由折叠可得，CFE GFE ∠∠=，由AD//BC ，可得CFE GEF ∠∠=，依据三角形外角性质得到1AEF GFE AGH 352∠∠∠===．【详解】如图，C'D'//AC ，，又DAC 20∠=，AGH 70∠∴=，由折叠可得，CFE GFE ∠∠=，由AD//BC ，可得CFE GEF ∠∠=，1AEF GFE AGH 352∠∠∠∴===，故选：B ．【点睛】本题主要考查了平行线的性质以及三角形外角性质的运用，解题时注意：两直线平行，内错角相等．9．如图，将一张三角形纸片ABC 的一角折叠，使点A 落在ABC ∆处的'A 处，折痕为DE .如果A α∠=，'CEA β∠=，'BDA γ∠=，那么下列式子中正确的是（）A ．2γαβ=+B ．2γαβ=+C ．γαβ=+D ．180γαβ=--【答案】A【解析】【分析】【详解】分析:根据三角形的外角得：∠BDA'=∠A+∠AFD ，∠AFD=∠A'+∠CEA'，代入已知可得结论. 详解:由折叠得：∠A=∠A'，∵∠BDA'=∠A+∠AFD ，∠AFD=∠A'+∠CEA'，∵∠A=α，∠CEA′=β，∠BDA'=γ，∴∠BDA'=γ=α+α+β=2α+β，故选A.点睛：本题考查了三角形外角的性质，熟练掌握三角形的外角等于与它不相邻的两个内角的和是关键.10．如图，将一张含有30角的三角形纸片的两个顶点叠放在矩形的两条对边上，若244∠=，则1∠的大小为（）A ．14B ．16C ．90α-D ．44α-【答案】A【解析】分析：依据平行线的性质，即可得到∠2=∠3=44°，再根据三角形外角性质，可得∠3=∠1+30°，进而得出结论．详解：如图，∵矩形的对边平行，∴∠2=∠3=44°，根据三角形外角性质，可得：∠3=∠1+30°，∴∠1=44°﹣30°=14°．故选A．点睛：本题主要考查了平行线的性质以及三角形外角性质的运用，解题时注意：两直线平行，同位角相等．11．如图，把一副三角板的两个直角三角形叠放在一起，则α的度数（）A．75°B．135°C．120°D．105°【答案】D【解析】如图，根据三角板的特点，可知∠3=45°，∠1=60°，因此可知∠2=45°，再根据三角形的外角的性质，可求得∠α=105°.故选12．已知三角形的两边长分别为4和9,则下列数据中能作为第三边长的是( )A．13 B．6 C．5 D．4【答案】B【解析】【分析】首先根据三角形的三边关系定理,求得第三边的取值范围,再进一步找到符合条件的数值．【详解】解：设这个三角形的第三边为x．根据三角形的三边关系定理“两边之和大于第三边，两边之差小于第三边”,得：94x94-<<+,解得5x13<<．故选：B．【点睛】本题考查了三角形的三边关系定理.一定要注意构成三角形的条件：两边之和>第三边,两边之差<第三边．三、八年级数学全等三角形填空题（难）13．如图,C为线段AE上一动点(不与A． E重合),在AE同侧分别作等边△ABC和等边△CDE,AD与BE交于点O,AD与BC交于点P,BE与CD交于点Q,连接PQ,以下五个结论：①AD=BE;②PQ∥AE;③CP=CQ;④BO=OE;⑤∠AOB=60°，一定成立的有________（填序号）【答案】①②③⑤【解析】【分析】①根据全等三角形的判定方法，证出△ACD≌△BCE，即可得出AD=BE．③先证明△ACP≌△BCQ，即可判断出CP=CQ，③正确；②根据∠PCQ=60°，可得△PCQ为等边三角形，证出∠PQC=∠DCE=60°，得出PQ∥AE，②正确．④没有条件证出BO=OE，得出④错误；⑤∠AOB=∠DAE+∠AEO=∠DAE+∠ADC=∠DCE=60°，⑤正确；即可得出结论．【详解】解：∵△ABC和△CDE都是等边三角形，∴AC=BC，CD=CE，∠ACB=∠DCE=60°，∴∠ACB+∠BCD=∠DCE+∠BCD，∴∠ACD=∠BCE，在△ACD和△BCE中，AC BCACD BCECD CE=⎧⎪∠=∠⎨⎪=⎩，∴△ACD≌△BCE（SAS），∴AD=BE，结论①正确．∵△ACD≌△BCE，∴∠CAD=∠CBE，又∵∠ACB=∠DCE=60°，∴∠BCD=180°-60°-60°=60°，∴∠ACP=∠BCQ=60°，在△ACP和△BCQ中，ACP BCQCAP CBQAC BC∠=∠⎧⎪∠=∠⎨⎪=⎩，∴△ACP≌△BCQ（AAS），∴CP=CQ，结论③正确；又∵∠PCQ=60°，∴△PCQ为等边三角形，∴∠PQC=∠DCE=60°，∴PQ∥AE，结论②正确．∵△ACD≌△BCE，∴∠ADC=∠AEO，∴∠AOB=∠DAE+∠AEO=∠DAE+∠ADC=∠DCE=60°，∴结论⑤正确．没有条件证出BO=OE，④错误；综上，可得正确的结论有4个：①②③⑤．故答案是：①②③⑤．【点睛】此题是三角形综合题目，考查了全等三角形的判定和性质的应用、等边三角形的性质和应用、平行线的判定；熟练掌握等边三角形的性质，证明三角形全等是解决问题的关键．14．如图，AB∥CD，O为∠BAC、∠ACD的平分线的交点，OE⊥AC于E，且OE=1，则AB与CD 之间的距离等于____．【答案】2【解析】过点O作OF⊥AB于F，作OG⊥CD于G，∵O为∠BAC、∠DCA的平分线的交点，OE⊥AC，∴OE=OF，OE=OG，∴OE=OF=OG=1，∵AB∥CD，∴∠BAC+∠ACD=180°，∴∠EOF+∠EOG=（180°﹣∠BAC）+（180°﹣∠ACD）=180°，∴E、O、G三点共线，∴AB与CD之间的距离=OF+OG=1+1=2．故答案为：2．点睛：本题考查了角平分线上的点到角的两边的距离相等的性质，平行线的性质，熟记性质是解题的关键，难点在于作出辅助线并证明E、O、G三点共线．15．在数学活动课上，小明提出这样一个问题：∠B＝∠C＝90°，E是BC的中点，DE平分∠ADC，∠CDE＝55°．如图，则∠EAB的度数为_________【答案】35°【解析】【分析】过点E作EF⊥AD于F，根据角平分线上的点到角的两边的距离相等可得CE=EF，再根据到角的两边距离相等的点在角的平分线上可得AE是∠BAD的平分线，然后求出∠AEB，再根据直角三角形两锐角互余求解即可．【详解】过点E作EF⊥AD于F．∵DE平分∠ADC，∴CE=EF．∵E是BC的中点，∴CE=BE，∴BE=EF，∴AE是∠BAD的平分线，∴∠EAB=∠FAE．∵∠B=∠C=90°，∴∠CDA+∠DAB=180°，∴2∠CDE+2∠EAB=180°，∴∠CDE+∠EAB=90°，∴∠EAB=90°－∠CDE=90°－55°=35°．故答案为：35°．【点睛】本题考查了角平分线上的点到角的两边的距离相等的性质，角平分线的判定，熟记性质并作辅助线是解题的关键．16．已知在△ABC 中,两边AB、AC的中垂线，分别交BC于E、G．若BC＝12，EG＝2，则△AEG的周长是________．【答案】16或12．【解析】【分析】根据线段垂直平分线性质得出AE=BE，CG=AG，分两种情况讨论：①DE和FG的交点在△ABC内，②DE和FG的交点在△ABC外．【详解】∵DE，FG分别是△ABC的AB，AC边的垂直平分线，∴AE=BE，CG=AG．分两种情况讨论：①当DE和FG的交点在△ABC内时，如图1．∵BC=12，GE=2，∴AE+AG=BE+CG=12+2=14，△AGE的周长是AG+AE+EG=14+2=16．②当DE和FG的交点在△ABC外时，如图2，△AGE的周长是AG+AE+EG= BE+CG+EG=BC=12．故答案为：16或12．【点睛】本题考查了线段垂直平分线性质，注意：线段垂直平分线上的点到线段两个端点的距离相等．17．如图，在ABC中，ACB90,CA CB∠==.点D在AB上，点F在CA的延长线上，连接FD并延长交BC于点E，若∠BED=2∠ADC，AF=2，DF=7，则ABC的面积为______．【答案】25 2【解析】【分析】作CD的垂直平分线交AD于M，交CD与N，根据垂直平分线的性质可得MC=MD，进而可得∠MDC=∠MCD，根据已知及外角性质可得∠AMC=∠BED，由等腰直角三角形的性质可得∠B=∠CAB=45°，根据三角形内角和定理可得∠ACM=∠BDE，进而可证明∠ADF=∠ACM，进而即可证明∠FCD=∠FDC，根据等腰三角形的性质可得CF=DF，根据已知可求出AC的长，根据三角形面积公式即可得答案.【详解】作CD的垂直平分线交AD于M，交CD与N，∵MN是CD的垂直平分线，∴MC=MD，∴∠MDC=∠MCD，∵∠AMC=∠MDC=∠MCD，∴∠AMC=2∠ADC，∵∠BED=2∠ADC，∴∠AMC=∠BED，∵∠ACB=90°，AC=BC，∴∠B=∠CAB=45°，∵∠ACM=180°-∠CAM-∠AMC，∠BDE=180°-∠B-∠BED，∴∠ACM=∠BDE，∵∠BDE=∠ADF，∴∠ADF=∠ACM，∴∠ADF+∠ADC=∠ACM+∠MCD，即∠FCD=∠FDC，∴FC=FD，∵AF=2，FD=7，∴AC=FC-AF=7-2=5，∴S△ABC=12×5×5=252.故答案为：25 2【点睛】本题考查了等腰三角形的判定与性质及线段垂直平分线的性质，线段垂直平分线上的点，到线段两端的距离相等；等腰三角形的两个底角相等；熟练掌握相关的定理及性质是解题关键.18．已知AD是△ABC的边BC上的中线，若AB = 4，AC = 6，则AD的取值范围是___________．【答案】15AD <<【解析】延长AD 到点E ，使DE=AD ，连接BE ，则可用SAS 证明△DAC ≌△DEB ，所以BE=AC. △ABE 中，BE-AB ＜AE ＜BE+AB ，即6-4＜AE ＜6+4，所以2＜AE ＜10.又AE=2AD ，所以2＜2AD ＜10，则1＜AD ＜5.故答案为1＜AD ＜5.点睛：本题主要考查了三角形的三边关系，即三角形的两边之和大于第三边，两边之差小于第三边，当题目中有三角形的中线时，如果需要添加辅助线，一般考虑把中线延长一倍（通常称“倍中线法”），构造全等三角形，将已知条件或要解决的问题集中到一个三角形中.四、八年级数学全等三角形选择题（难）19．如图是由4个相同的小正方形组成的网格图，其中∠1+∠2等于（）A ．150°B ．180°C ．210°D ．225°【答案】B【解析】【分析】根据SAS 可证得ABC ≌EDC ，可得出BAC DEC ∠∠=，继而可得出答案，再根据邻补角的定义求解.【详解】由题意得：AB ED =，BC DC =，D B 90∠∠==，ABC ∴≌EDC ， BAC DEC ∠∠∴=，12180∠∠+=．故选B ．【点睛】本题考查全等图形的知识，比较简单，解答本题的关键是判断出ABC ≌EDC ．.20．如图，C 为线段AE 上一动点（不与点A 、E 重合），在AE 同侧分别作等边三角形ABC 和等边三角形CDE ，AD 与BE 交于点O ，AD 与BC 交于点P ，BE 与CD 交于点Q ，连接PQ ．以下五个结论：①AD ＝BE ；②AP ＝BQ ；③PQ ∥AE ；④DE ＝DP ；⑤∠AOE ＝120°；其中正确结论的个数为（）A ．2个B ．3个C ．4个D ．5个【答案】C【解析】【分析】 ①由于△ABC 和△CDE 是等边三角形，可知AC=BC ，CD=CE ，∠ACB=∠DCE=60°，从而证出△ACD ≌△BCE ，可推知AD=BE ，故①正确；②由△ACD ≌△BCE 得∠CBE=∠DAC ，加之∠ACB=∠DCE=60°，AC=BC ，得到△ACP ≌△BCQ （ASA ），所以AP=BQ ；故②正确；③根据②△CQB ≌△CPA （ASA ），再根据∠PCQ=60°推出△PCQ 为等边三角形，又由∠PQC=∠DCE ，根据内错角相等，两直线平行，可知③正确；④根据∠QCP=60°，∠DPC=∠BCA+∠PAC ＞60°，可知PD≠CD ，可知④错误；⑤利用等边三角形的性质，BC ∥DE ，再根据平行线的性质得到∠CBE=∠DEO ，于是∠AOB=∠DAC+∠BEC=∠BEC+∠DEO=∠DEC=60°，由平角的性质可得∠AOE=120°，可知⑤正确；【详解】①∵△ABC 和△CDE 为等边三角形∴AC ＝BC ，CD ＝CE ，∠BCA ＝∠DCB ＝60°∴∠ACD ＝∠BCE∴△ACD ≌△BCE （SAS ）∴AD ＝BE ，故①正确；由（1）中的全等得∠CBE ＝∠DAC ，且BC ＝AC ，∠ACB ＝∠BCQ ＝60°∴△CQB ≌△CPA （ASA ），∴AP ＝BQ ，故②正确；∵△CQB ≌△CPA ，∴PC ＝PQ ，且∠PCQ ＝60°∴△PCQ 为等边三角形，∴∠PQC ＝∠DCE ＝60°，∴PQ ∥AE ，故③正确，∵∠QCP ＝60°，∠DPC ＝∠BCA +∠PAC ＞60°，∴PD ≠CD ，∴DE ≠DP ，故④DE ＝DP 错误；∵BC ∥DE ，∴∠CBE ＝∠BED ，∵∠CBE ＝∠DAE ，∴∠AOB ＝∠OAE +∠AEO ＝60°，∴∠AOE ＝120°，故⑤正确，故选C ．【点睛】本题考查了全等三角形的判定与性质，利用了等边三角形的判定与性质，全等三角形的判定与性质，平行线的判定与性质，综合性较强，题目难度较大．21．如图，在▱ABCD 中，AD =2AB ，F 是AD 的中点，作CE ⊥AB ，垂足E 在线段AB 上，连接EF 、CF ，则下列结论中①∠DCF =123,1x x ==-∠BCD ；②EF =CF ；③S △BEC =2S △CEF ；④∠DFE =3∠AEF ．一定成立的是（）A ．①②B ．①③④C ．①②③D ．①②④【答案】D【解析】①∵F 是AD 的中点，∴AF=FD ， ∵在?ABCD 中，AD=2AB ，∴AF=FD=CD ，∴∠DFC=∠DCF ，∵AD ∥BC ，∴∠DFC=∠FCB，∴∠DCF=∠BCF，∴∠DCF=12∠BCD，故此选项正确；延长EF，交CD延长线于M，∵四边形ABCD是平行四边形，∴AB∥CD，∴∠A=∠MDF，∵F为AD中点，∴AF=FD，在△AEF和△DFM中，∠A＝∠FDMAF＝DF∠AFE＝∠DFM，∴△AEF≌△DMF（ASA），∴FE=MF，∠AEF=∠M，∵CE⊥AB，∴∠AEC=90°，∴∠AEC=∠ECD=90°，∵FM=EF，∴FC=FM，故②正确；③∵EF=FM，∴S△EFC=S△CFM，∵MC＞BE，∴S△BEC＜2S△EFC故S△BEC=2S△CEF错误；④设∠FEC=x，则∠FCE=x，∴∠DCF=∠DFC=90°-x，∴∠EFC=180°-2x，∴∠EFD=90°-x+180°-2x=270°-3x，∵∠AEF=90°-x，∴∠DFE=3∠AEF，故此选项正确．故正确的有：①②④．故选D.22．如图，BD是∠ABC的角平分线，AD⊥AB，AD=3，BC=5，则△BCD的面积为（）A．7.5 B．8 C．10D．15【答案】A【解析】作DE⊥BC于E，根据角平分线的性质，由BD是∠ABC的角平分线，AD⊥AB，DE⊥BC，求出DE=DA=3，根据三角形面积公式计算S△BCD=12×BC×DE=7.5，故选：A．23．如图，已知等腰Rt△ABC和等腰Rt△ADE，AB=AC=4，∠BAC=∠EAD=90°，D是射线BC 上任意一点，连接EC．下列结论：①△AEC△ADB；②EC⊥BC ；③以A、C、D、E为顶点的四边形面积为8；④当BD=时，四边形AECB的周长为10524++;⑤当BD=32B时,ED=5AB；其中正确的有（）A．5个 B．4个 C．3 个 D．2个【答案】B【解析】解：∵∠BAC=∠EAD=90°，∴∠BAD=∠CAE，∵AB=AC，AD=AE，∴△AEC≌△ADB，故①正确；∵△AEC≌△ADB，∴∠ACE=∠ABD=45°，∵∠ACB=45°，∴J IAO ECB=90°，∴EC⊥BC，故②正确；∵四边形ADCE的面积=△ADC的面积+△ACE的面积=△ADC的面积+△ABD的面积=△ABC 的面积=4×4÷2=8．故③正确；∵BD =2，∴EC =2，DC =BC -BD =422-=32，∴DE 2=DC 2+EC 2，=()()22322+=20，∴DE =25，∴AD =AE =252=10.∴AECB 的周长=AB +DC +CE +AE =442210+++=45210++，故④正确；当BD =32BC 时，CD =12BC ，∴DE =221322BC BC ⎛⎫⎛⎫+ ⎪ ⎪⎝⎭⎝⎭=10BC =5AB ．故⑤错误．故选B ．点睛：此题是全等三角形的判定与性质的综合运用，熟练掌握等腰直角三角形的性质是解答此题的关键．24．如图,在△ABC 中,∠C=90°,∠B=30°,以A 为圆心,任意长为半径画弧分别交AB,AC 于点M 和N,再分别以M,N 为圆心,大于12MN 的长为半径画弧,两弧交于点P,连结AP 并延长交BC 于点D,则下列说法中正确的个数是( )①AD 平分∠BAC；②作图依据是S.A ．S ；③∠ADC=60°； ④点D 在AB 的垂直平分线上A ．1个B ．2个C ．3个D ．4个【答案】C【解析】 ①根据作图的过程可以判定AD 是∠BAC 的∠平分线；②根据作图的过程可以判定出AD 的依据；③利用角平分线的定义可以推知∠CAD=30°，则由直角三角形的性质求∠ADC 的度数； ④利用等角对等边可以证得△ADB 的等腰三角形，由等腰三角形的“三合一”的性质可以证明点在AB 的中垂线上.解：如图所示，①根据作图的过程可知，AD 是∠BAC 的∠平分线；故①正确；②根据作图的过程可知，作出AD 的依据是SSS ；故②错误；③∵在△ABC 中，∠C=90°，∠B=30°，∴∠CBA=60°.又∵AD 是∠BAC 的平分线，∴∠1=∠2=12∠CAB=30°， ∴∠3=90°-∠2=60°，即∠ADC=60°.故③正确；④∵∠1=∠B=30°，∴AD=BD，∴点D 在AB 的中垂线上.故④正确；故选C.“点睛”此题主要考查的是作图-基本作图，涉及到角平分线的作法以及垂直平分线的性质，熟练根据角平分线的性质得出∠ADC 的度数是解题的关键.五、八年级数学轴对称三角形填空题（难）25．如图，在ABC 中，点A 的坐标为()0,1，点B 的坐标为()0,4，点C 的坐标为()4,3，点D 在第二象限，且ABD 与ABC 全等，点D 的坐标是______．【答案】(－4，2)或(－4，3)【解析】【分析】【详解】把点C 向下平移1个单位得到点D （4，2），这时△ABD 与△ABC 全等，分别作点C ，D 关于y 轴的对称点（-4，3）和（-4，2），所得到的△ABD 与△ABC 全等.故答案为(－4，2)或(－4，3).26．在平面直角坐标系xOy 中，已知点A （2，3），在x 轴上找一点P ，使得△AOP 是等腰三角形，则这样的点P 共有_____个．【答案】4【解析】【分析】以O为圆心，OA为半径画弧交x轴于点P1、P3，以A为圆心，AO为半径画弧交x轴于点P4，作OA的垂直平分线交x轴于P2．【详解】解：如图，使△AOP是等腰三角形的点P有4个．故答案为4．【点睛】本题考查了在平面直角坐标系中寻找等腰三角形，掌握两圆一线找等腰三角形是解题的关键．27．在平面直角坐标系中，点A在x轴的正半轴上，点B在y轴的正半轴上，∆为等腰三角形，符合条件的C点有∠=︒，在x轴或y轴上取点C，使得ABC36ABO__________个．【答案】8【解析】【分析】观察数轴，按照等腰三角形成立的条件分析可得答案．【详解】解：如下图所示，若以点A为圆心，以AB为半径画弧，与x轴和y轴各有两个交点，但其中一个会与点B重合，故此时符合条件的点有3个；若以点B为圆心，以AB为半径画弧，同样与x轴和y轴各有两个交点，但其中一个与点A重合，故此时符合条件的点有3个；线段AB的垂直平分线与x轴和y轴各有一个交点，此时符合条件的点有2个．∴符合条件的点总共有：3＋3＋2=8个．故答案为：8．【点睛】本题考查了等腰三角形的判定，可以观察图形，得出答案．28．如图,A,B,C三点在同一直线上,分别以AB,BC（AB>BC）为边,在直线AC的同侧作等边ΔABD和等边ΔBCE,连接AE交BD于点M,连接CD交BE于点N,连接MN. 以下结论：①AE=DC，②MN//AB，③BD⊥AE，④∠DPM=60°，⑤ΔBMN是等边三角形.其中正确的是__________（把所有正确的序号都填上）.【答案】①②④⑤【解析】【分析】①由三角形ABD与三角形BCE都为等边三角形，利用等边三角形的性质得到两条边对应相等，两个角相等都为60°，利用SAS即可得到三角形ABE与三角形DBC全等即可得结论；②由①中三角形ABE与三角形DBC全等，利用全等三角形的对应角相等得到一对角相等，再由∠ABD=∠EBC=60°，利用平角的定义得到∠MBE=∠NBC=60°，再由EB=CB，利用ASA 可得出三角形EMB与三角形CNB全等，利用全等三角形的对应边相等得到MB=NB，再由∠MBE=60°，利用有一个角为60°的等腰三角形为等边三角形可得出三角形BMN为等边三角形；可得∠BMN=60°，进行可得∠BMN=∠ABD，故MN//AB，从而可判断②，⑤正确；③无法证明PM=PN，因此不能得到BD⊥AE；④由①得∠EAB=∠CDB，根据三角形内角和和外角的性质可证得结论.【详解】①∵等边△ABD和等边△BCE，∴AB=DB，BE=BC，∠ABD=∠EBC=60°，∴∠ABE=∠DBC=120°，在△ABE和△DBC中，∵AB DBABE DBC BE BC⎪∠⎪⎩∠⎧⎨＝＝＝，∴△ABE≌△DBC（SAS），∴AE=DC，故①正确；∵△ABE≌△DBC，∴∠AEB=∠DCB，又∠ABD=∠EBC=60°，∴∠MBE=180°-60°-60°=60°，即∠MBE=∠NBC=60°，在△MBE和△NBC中，∵AEB DCB EB CBMBE NBC ∠∠∠⎧⎪⎪⎩∠⎨＝＝＝，∴△MBE≌△NBC（ASA），∴BM=BN，∠MBE=60°，则△BMN为等边三角形，故⑤正确；∵△BMN为等边三角形，∴∠BMN=60°,∵∠ABD=60°,∴∠BMN=∠ABD，∴MN//AB，故②正确；③无法证明PM=PN，因此不能得到BD⊥AE；④由①得∠EAB=∠CDB，∠APC+∠PAC+∠PCA=180°，∴∠PAC+∠PCA=∠PDB+∠PCB=∠DBA=60°，∵∠DPM =∠PAC+∠PCA∴∠DPM =60°，故④正确，故答案为：①②④⑤.【点睛】此题考查了等边三角形的判定与性质，以及全等三角形的判定与性质，熟练掌握判定与性质是解本题的关键．29．如图，BD 是ABC 的角平分线，AE BD ⊥，垂足为F ，且交线段BC 于点E ，连结DE ，若50C ∠=︒，设 ABC x CDE y ∠=︒∠=︒,，则y 关于x 的函数表达式为_____________．【答案】80y x =-【解析】【分析】根据题意，由等腰三角形的性质可得BD 是AE 的垂直平分线，进而得到AD ＝ED ，求出BED ∠的度数即可得到y 关于x 的函数表达式．【详解】∵BD 是ABC ∆的角平分线，AE BD ⊥∴1122ABD EBD ABC x ∠=∠=∠=︒，90AFB EFB ∠=∠=︒ ∴1902BAF BEF x ∠=∠=︒-︒ ∴AB BE =∴AF EF =∴AD ED =∴DAF DEF ∠=∠∵180BAC ABC C ∠=︒-∠-∠，50C ∠=︒∴130BAC x ∠=︒-︒∴130BED BAD x ∠=∠=︒-︒∵CDE BED C ∠=∠-∠∴1305080y x x ︒=-︒-︒=︒-︒∴80y x =-，故答案为：80y x =-．【点睛】本题主要考查了等腰三角形的性质及判定，三角形的内角和定理，三角形外角定理，角的和差倍分等相关知识，熟练运用角的计算是解决本题的关键．30．如图,在ABC 中, 90,ACB ABD ︒∠=是ABC 的轴对称图形,点E 在AD 上,点F 在AC 的延长线上.若点B 恰好在EF 的垂直平分线上,并且5AE =,13AF =,则DE =______．【答案】4．【解析】【分析】连接BE ，BF ，根据轴对称的性质可得△ABD ≌△ACB ，进而可得DB=CB ，AD=AC ，∠D=∠BCA=90°，再利用线段垂直平分线的性质可得BE=BF ，然后证明Rt △DBE ≌Rt △CBF 可得DE=CF ，然后可得ED 长．【详解】解：连接BE ，BF ，∵△ABD 是△ABC 的轴对称图形，∴△ABD ≌△ACB ，∴DB=CB ，AD=AC ，∠D=∠BCA=90°，∴∠BCF=90°，∵点B 恰好在EF 的垂直平分线上，∴BE=BF ，在Rt △DBE 和Rt △CBF 中BD BC EB FB =⎧⎨=⎩，∴Rt △DBE ≌Rt △CBF （HL ），∴DE=CF ，设DE=x ，则CF=x ，∵AE=5，AF=13，∴AC=AD=5+x ，∴AF=5+2x ，∴5+2x=13，∴x=4，∴DE=4，故答案为：4．【点睛】此题主要考查了轴对称和线段垂直平分线的性质，关键是掌握成轴对称的两个图形全等．六、八年级数学轴对称三角形选择题（难）31．如图，ABC ∆中，60BAC ∠=︒，BAC ∠的平分线AD 与边BC 的垂直平分线MD 相交于点D ，DE AB ⊥交AB 的延长线于点E ，DF AC ⊥于点F ，现有下列结论：①DE DF =；②DE DF AD +=；③DM 平分EDF ∠；④2AB AC AE +=，其中正确的是（）A ．①②B ．①②③C ．①②④D ．①②③④【答案】C【解析】【分析】 ①由角平分线的性质可知①正确；②由题意可知∠EAD=∠FAD=30°，故此可知ED=12AD ，DF=12AD ，从而可证明②正确；③若DM 平分∠EDF ，则∠EDM=90°，从而得到∠ABC 为直角三角形，条件不足，不能确定，故③错误；④连接BD 、DC ，然后证明△EBD ≌△DFC ，从而得到BE=FC ，从而可证明④．【详解】解：如图所示：连接BD 、DC ．①∵AD 平分∠BAC ，DE ⊥AB ，DF ⊥AC ，∴ED=DF ．∴①正确．②∵∠EAC=60°，AD 平分∠BAC ，∴∠EAD=∠FAD=30°．∵DE ⊥AB ，∴∠AED=90°．∵∠AED=90°，∠EAD=30°， ∴ED=12AD ．同理：DF=12AD ． ∴DE+DF=AD ．∴②正确． ③由题意可知：∠EDA=∠ADF=60°．假设MD 平分∠EDF ，则∠ADM=30°．则∠EDM=90°，又∵∠E=∠BMD=90°，∴∠EBM=90°．∴∠ABC=90°．∵∠ABC 是否等于90°不知道，∴不能判定MD 平分∠EDF ，故③错误．④∵DM 是BC 的垂直平分线，∴DB=DC ．在Rt △BED 和Rt △CFD 中DE DF BD DC ⎧⎨⎩＝＝， ∴Rt △BED ≌Rt △CFD ．∴BE=FC ．∴AB+AC=AE-BE+AF+FC又∵AE=AF ，BE=FC ，∴AB+AC=2AE ．故④正确．综上所述，①②④正确，故选：C．【点睛】本题主要考查的是全等三角形的性质和判定、角平分线的性质、线段垂直平分线的性质，掌握本题的辅助线的作法是解题的关键．32．如图，△ABC是等边三角形，AQ＝PQ，PR⊥AB于点R，PS⊥AC于点S，PR＝PS，则下列结论：①AP⊥BC；②AS＝AR；③QP∥AR；④△BRP≌△QSP.正确的有( )A．1个B．2个C．3个D．4个【答案】D【解析】【分析】根据到角的两边的距离相等的点在角的平分线上可得AP平分∠BAC，根据等腰三角形“三线合一”的性质判断出①正确；根据HL证明Rt△APR≌Rt△APS，即可判断②正确；根据等边对等角的性质可得∠APQ=∠PAQ，根据三角形外角的性质得到然后得到∠PQC=2∠PAC=60°=∠BAC，然后根据同位角相等两直线平行可得QP∥AB，从而判断出③正确，④由③易证△QPC是等边三角形，得到PQ=PC，等量代换得到BP=PQ，用HL证明Rt△BRP≌Rt△QSP，即可得到④正确．【详解】∵△ABC是等边三角形，PR⊥AB，PS⊥AC，且PR=PS，∴P在∠A的平分线上．∵AB=AC，∴AP⊥BC，故①正确；∵PA=PA，PR=PS，∴Rt△APR≌Rt△APS，∴AS=AR，故②正确；∵AQ=PQ，∴∠APQ=∠PAQ，∴∠PQC=2∠PAC=60°=∠BAC，∴PQ∥AR，故③正确；由③得：△PQC是等边三角形，∴△PQS≌△PCS，∴PQ=PC．又∵AB=AC，AP⊥BC，∴BP=PC，∴BP=PQ．∵PR=PS，∴Rt△BRP≌Rt△QSP，故④也正确．∵①②③④都正确．故选D．【点睛】本题考查了等腰三角形的性质、全等三角形的判定与性质以及等边三角形的判定与性质，准确识图并熟练掌握全等三角形的判定方法与性质是解题的关键．33．如图, 在△DAE中, ∠DAE＝40°, B、C两点在直线DE上，且∠BAE＝∠BEA，∠CAD＝∠CDA，则∠BAC的大小是（）A．100°B．90°C．80°D．120°【答案】A【解析】【分析】由已知条件，利用了中垂线的性质得到线段相等及角相等，再结合三角形内角和定理求解.【详解】解：如图，∵BG是AE的中垂线，CF是AD的中垂线，∴AB=BE，ACECD∴∠AED=∠BAE=∠BAD+∠DAE，∠CDA=∠CAD=∠DAE+∠CAE，∵∠DAE+∠ADE+∠AED=180°∴∠BAD+∠DAE+∠DAE+∠CAE+∠DAE=3∠DAE+∠BAD+∠EAC=120°+∠BAD+∠EAC=180°∴∠BAD+∠EAC=60°∴.∠BAC=∠BAD+∠EAC+∠DAE=60°+40°=100°；故选：A【点睛】本题考查了中垂线的性质、三角形内角和定理及等腰三角形的判定与性质；找着各角的关系利用内角和列式求解是正确解答本题的关键.34．如图，已知等边△ABC的面积为43， P、Q、R分别为边AB、BC、AC上的动点，则PR＋QR的最小值是（）A．3B．3C15D．4【答案】B【解析】如图，作△ABC 关于AC 对称的△ACD ，点E 与点Q 关于AC 对称，连接ER ，则QR=ER ，当点E ，R ，P 在同一直线上，且PE ⊥AB 时，PE 的长就是PR +QR 的最小值，设等边△ABC 的边长为x ，则高为32x ， ∵等边△ABC 的面积为43，∴12x ×32x=43，解得x=4， ∴等边△ABC 的高为32x=23，即PE=23，所以PR +QR 的最小值是23，故选B.【点睛】本题考查了轴对称的性质，最短路径问题等，解题的关键是正确添加辅助线构造出最短路径.35．如图，已知，点A （0，0）、B （43，0）、C （0，4），在△ABC 内依次作等边三角形，使一边在x 轴上，另一个顶点在BC 边上，作出的等边三角形分别是第1个△AA 1B 1，第2个△B 1A 2B 2，第3个△B 2A 3B 3，…则第2017个等边三角形的边长等于（）A ．201532 B ．201632 C ．2017327 D ．201932【答案】A【解析】【分析】【详解】根据锐角三函数的性质，由OB=3OC=1，可得∠OCB=90°，然后根据等边三角形的性质，可知∠A 1AB=60°，进而可得∠CAA 1=30°，∠CA 1O=90°，因此可推导出∠A 2A 1B=30°，同。

公共场所的英文标语30个

公共场所的英文标语30个1. Please keep off the grass. 请不要践踏草坪。

2. Keep in quiet hours. 请在静音时段保持安静。

3. No smoking in the public place. 请勿在公共场所吸烟。

4. No littering, please. 请勿乱扔垃圾。

5. Respect others and yourself. 尊重他人就是尊重自己。

6. Please queue up. 请排队等候。

7. Mind the gap. 请注意台阶缝隙。

8. Keep your hands to yourself. 请勿动手动脚。

9. Please use the escalator. 请使用扶梯。

10. Please use the door, don't break it. 请用门，不要破坏。

11. Please don't lean on the elevator door. 请勿依靠电梯门。

12. Mind your head. 请注意头顶。

13. Please keep clear of the emergency exits. 请勿占用紧急出口。

14. Please take care of your personal belongings. 请保管好个人物品。

15. Please show your ticket/boarding pass. 请出示车票/登机牌。

16. Please wait for your turn to board the plane/train. 请排队等待登机/火车。

17. Please fasten your seat belt. 请系好安全带。

18. Please don't block the aisle. 请勿堵塞通道。

19. Keep off the road/pathway, please. 请勿在道路上/通道上行走。

图书馆的提示语

图书馆的提示语（最新版）编制人：__________________审核人：__________________审批人：__________________编制单位：__________________编制时间：____年____月____日序言下载提示：该文档是本店铺精心编制而成的，希望大家下载后，能够帮助大家解决实际问题。

文档下载后可定制修改，请根据实际需要进行调整和使用，谢谢!并且，本店铺为大家提供各种类型的经典范文，如演讲稿、总结报告、合同协议、方案大全、工作计划、学习计划、条据书信、致辞讲话、教学资料、作文大全、其他范文等等，想了解不同范文格式和写法，敬请关注!Download tips: This document is carefully compiled by this editor.I hope that after you download it, it can help you solve practical problems. The document can be customized and modified after downloading, please adjust and use it according to actual needs, thank you!In addition, this shop provides you with various types of classic sample essays, such as speech drafts, summary reports, contract agreements, project plans, work plans, study plans, letter letters, speeches, teaching materials, essays, other sample essays, etc. Want to know the format and writing of different sample essays, so stay tuned!图书馆的提示语安全记心中，平安行途中，幸福驻家中。

学校图书馆提示语80句精选

学校图书馆提示语80句精选（最新版）编制人：__________________审核人：__________________审批人：__________________编制单位：__________________编制时间：____年____月____日序言下载提示：该文档是本店铺精心编制而成的，希望大家下载后，能够帮助大家解决实际问题。

文档下载后可定制修改，请根据实际需要进行调整和使用，谢谢!并且，本店铺为大家提供各种类型的实用范文，如宣传用语、心得体会、导游词大全、合同范本、致辞讲话、演讲稿大全、个人报告、工作资料、条据书信、办公文秘、其他范文等等，想了解不同范文格式和写法，敬请关注!Download tips: This document is carefully compiled by this editor.I hope that after you download it, it can help you solve practical problems. The document can be customized and modified after downloading, please adjust and use it according to actual needs, thank you!In addition, this shop provides you with various types of practical sample essays, such as propaganda language, experience, guide words, contract templates, speeches, speech drafts, personal reports, work materials, letter letters, office secretaries, and other sample essays Wait, if you want to know the format and writing of different sample essays, stay tuned!学校图书馆提示语80句精选书山有路勤为径，学海无涯苦做舟。

图书馆的警示语英语

图书馆的警示语英语People to the line, the book to invalid。

你们想知道图书馆的警示语英语有哪些吗?下面，店铺整理了图书馆的警示语英语给大家，希望帮助大家。

图书馆的警示语英语(精选篇)1. Static to self-cultivation, to raise Germany.2. Civilization to borrow books, courtesy to return books3. There is no royal road to There is no end for learning. suffering for the boat4. On the ladder of progress, towards the other side of the soul.5. Do not leave a cloud in this piece of pure land6. Everyone needs to read, everyone must love books7. Life should be full of vitality, we should always be curious about literature8. The world glory, splendour, wealth and rank than a good book9. He will love the book, no non benevolent10. The sea bird and fish Tongxiang, you and I share the cultural knowledge11. The knowledge of people, human more perfect12. This moment will nap, you will have a dream but this moment study, you will interpret a dream.13. No mercy, mercy to men14. Books are the source of wisdom, and reading is the ladder of progress15. A beautiful woman in the book, the book house of gold 图书馆的标语英语(最新篇)1. Books are the source of wisdom, the ladder of progress2. Books make men wise and wise men3. There is no royal road to There is no end for learning. hard to do4. The book is a ready-made panacea, be learned in books all kinds of extinction5. Life, there must be wisdom forever support, life, to have knowledge often accompanied6. The investment future person will be, will be loyal to the reality person7. The knowledge of people, human more perfect.8. Two ears do not hear out of the window, only read the book9. Walk softly with lady style, line seat Sommersby Fangxian10. Has not been difficult, then does not have the harvest11. There is no need to speak too much in the mind12. Diffuse knowledge scholarly circle, Xuehai no cliffs I call the shots.13. Time the study pain is temporary, has not learned the pain islife long14. Without you, I'm so lonely, I want to book, come with me15. Books can be the soul of courtesy16. Laughter is valuable, the exchange price is higher, if it is quiet, the two can throw17. Life, there must be wisdom forever support, life, there is always accompanied by knowledge18. Take only full of knowledge, don't leave any regrets.19. Intentions to understand knowledge, care for books20. The sea bird and fish Tongxiang, you and I share the cultural knowledge.图书馆的温馨警示语英语(热门篇)1. Poetry is not heartless, an angel to protect it2. Educated is your right, love is your duty nurse book book3. Books can purify one's soul and improve one's accomplishments4. Civilization to borrow books, courtesy to return the book5. Books are the source of knowledge6. Diffuse knowledge scholarly circle, cliff Xuehai without me7. [net] to improve the static competitive performance, self-cultivation.8. Take a book, leaving room clean.9. There is no book in life, as if there is no sunlight; wisdom without books is like a bird without wings10. People to the line, the book to invalid11. The investment future person will be, will be loyal to the reality person12. The infiltration of books and life as the foundation; swim the sea, enjoy the pleasure of reading.13. Eye view ear to a quiet at all times and in all countries,14. The communication of the soul does not need too many words15. Not just romantic eloquence wins, taste the longest without words。

图书馆的警示语英文

图书馆的警示语英文At this time there is no sound wins sound。

你们听说图书馆的警示语英文有哪些吗?那么学识网小编为大家整理了图书馆的警示语英文，欢迎阅览!图书馆的警示语英文(热门) 1. Building a harmonious world of knowledge, reading achievements wonderful life2. Quiet atmosphere to create a warm environment, silent meditation gives you infinite wisdom.3. Educated is your right, love the book supporting book is your duty.4. Y ou gently come, just as you gently leave, and beneficial and harmless5. Gently I go, as I gently come, do not take a Book6. Handle with care, take care of the books7. Light needle inadvertently, landing sound, the gentleman intentionally, silent and not language8. Please give others a quiet space9. Time the study pain is temporary, has not learned the pain islife long10. The book is a magic weapon of selfcultivation, is the pillar ofthe human spirit.11. Not just romantic eloquence wins, silent taste is the longest.12. Static knowledge, maintenance on everyone13. No mercy to his mercy.14. Books are the ladder of human progress15. Static to selfcultivation, learn to moral education图书馆的标语英文(集锦) 1. tatic knowledge, maintenance by everyone2. Read ten thousand books, traveling thousands of miles.3. Confessions of the book: I hope that even though I have wrinkles, experienced the vicissitudes of life, you still take me as a treasure in the palm of your hand4. Books can make up for ignorance and ignorance5. Take away the knowledge, leaving behind civilization6. The civilization of China is more powerful, the civilized society is more harmonious, the civilized campus is more beautiful, the civilized library is more precious7. The bright classroom is my home, spacious and clean8. Handle with care, take care of the books.9. Books are the ever burning lamps of accumulated wisdom10. Books are friends of human beings11. Books are the ladder of human progress12. Books are the best nutritional supplement for people’s spiritual hunger13. A good book is the best of friends, today and tomorrow.14. Create a warm and comfortable environment, experience a different romantic life15. A sound more quiet, like thousands of knowledge to create a better environment.16. Y ou go quietly, as quietly as you came17. Silence has been raised here as a virtue18. At this time there is no sound wins sound19. Eye ear takes a moment alone. At all times and in all countries.20. Knowledge is the crystallization of precious stones, culture is the luster of the gem。

图书馆英语安全标

图书馆英语安全标1, the subordinates are merciful, books are also life.2, away from the city's propaganda, but also a peaceful mind.3, the sea of books, do not need the roar of the wind and waves; The sea of books, only with the heart can control it.4. In the library, you can only read, not read.5, reading is endless, "quiet" in the unspoken.6. To have a soul dialogue with a wise person, you only need to use a quiet heart.7, take the knowledge away, leave the quiet.8, love books in the heart.9. Thoughts are wandering between the eyes and the heart, please do not make a sound.10. Silent guidance, quiet pilot.11, less nonsense and silent reading, what you get is a peace.12, love books is also an attitude to life.13, silence is golden, keep quiet.14. Listen attentively to the voices around you.15, a gentleman loves books and keeps his mouth shut.16, silent understanding of life, only need the heart to tell.17. Give tranquility to others and keep civilization to yourself.18 No amount of words is as good as the hope that a lamp brings us.19 The communication of the mind does not require too many words.20, not saying a word, sometimes worth a thousand words.21. There is a road in the book mountain, everyone is progressing, and civilization is shared.22. Civilization spreads silently here.23. Don't use your mouth to read, but stay in your heart.24, whispering with books, not too many people need to know.25. Be quiet at all times of reading, and at this time silence is better than sound.。