九年级数学圆及旋转题库

serve her this time with great difficulty, he climbed into the shop window to get the dress. As soon as she saw it, the woman said s many ties.And a woman cant have too many hats, she answered.Ten minutes later we walked out of the shop together. My wife was wearing a hat that looked like a lighthouse !Lesson42 Not very musical 并非很懂音乐As we had had a long walk through one of the markets of Old Delhi, we stopped at a square to have a rest. After a time, we noticed a snake-charmer with two large baskets at the other side of the square, so we went to have a look at him. As soon as he saw us, he picked up a long pipe which was covered with coins and opened one of the baskets. When he began to play a tune, we had our first glimpse of the snake. It rose out of the basket and began to follow the movements of the pipe. We were very much surprised when the snake charmer suddenly began to play jazz tunes and modern pop songs. The snake, however, continued to dance slowly. It obviously could not tell the difference between Indian music and jazz!Lesson43 Over the South Pole 飞越南极In 1929, three years after his flight over the North Pole, the American explorer, R. E. Byrd, successfully flew over the South Pole for the first time. Though, at first, Byrd and his men were able to take a great many photographs of the mountains that lay below, they soon ran into serious trouble. At one point, it seemed certain that their plane would crash. It could only get over the mountains if it rose to 10,000 feet. Byrd at once ordered his men to throw out two heavy food sacks. The plane was then able to rise and it cleared the mountains by 400 feet. Byrd now knew that he would be able to reach the South Pole which was 300 miles away, for there were no more mountains in sight. The aircraft was able to fly over the endless white plains without difficulty. Lesson44 Through the forest 穿过森林Mrs Anne Sterling did not think of the risk she was taking when she ran through a forest after two men. They had rushed up to her while she was having a picnic at the edge of a forest with her children and tried to steal her handbag. In the struggle, the strap broke and, with the bag in their possession, both men started running through the trees. Mrs Sterling got so angry that she ran after them. She was soon out of breath, but she continued to run. When she caught up with them, she saw that they had sat down and were going through the contents of the bag, so she ran straight at them. The men got such a fright that they dropped the bag and ran away. The strap needs mending, said Mrs Sterling later, but they did not steal anything.Lesson45 A clear conscience 问心无愧The whole village soon learnt that a large sum of money had been lost. Sam Benton, the local butcher, had lost his wallet while taking his savings to the post-office. Sam was sure that the wallet must have been found by one of the villagers, but it was not returned to him. Three months passed, and then one morning, Sam found his wallet outside his front door. It had been wrapped up in newspaper and it contained half the money he had lost, together with a note which said: A thief, yes, but only 5o per cent a thief! Two months later, some more money was sent to Sam with another note: Only 25 per cent a thief now! In time, all Sams money was paid back in this way. The last note said: I am 100 per cent honest now!lesson46 Expensive and uncomfortable 既昂贵又受罪When a plane from London arrived at Sydney airport, workers began to unload a number of wooden boxes which contained clothing. No one could account for the fact that one of the boxes was extremely heavy. It suddenly occurred to one of the workers to open up the box. He was astonished at what he found. A man was lying in the box on top of a pile of woollen goods. He was so surprised at being discovered that he did not even try to run away. After he was arrested, the man admitted hiding in the box before the plane left London. He had had a long and uncomfortable trip, for he had been confined to the wooden box for over ten hours. The man was ordered to pay &345 for the cost of the trip. The normal price of a ticket is &230 !Lesson47 A thirsty ghost 嗜酒的鬼魂A public house which was recently bought by Mr Ian Thompson is up for sale. Mr Thompson is going to sell it because it is haunted. He told me that he could not go to sleep one night because he heard a strange noise coming from the bar. The next morning, he found that the doors had been blocked by chairs and the furniture had been moved. Though Mr Thompson had turned the lights off before he went to bed, they were on in the morning. He also said that he had found five empty whisky bottles which the ghost must have drunk the night before. When I suggested that some villagers must have come in for a free drink, Mr Thompson shook his head. The villagers have told him that they will not accept the inn even if he gives it away. Lesson48 Did you want to tell me something? 你想对我说什么吗？Dentists always ask questions when it is impossible for you to answer. My dentist had just pulled out one of my teeth and had told me to rest for a while. I tried to say something, but my mouth was full of cotton-wool. He knew I collected birds eggs and asked me whether my collection was growing. He then asked me how my brother was and whether I liked my new job in London. In answer to these questions I either nodded or made strange noises. Meanwhile, my tongue was busy searching out the hole where the tooth had been. I suddenly felt very worried, but could not say anything. When the dentist at last removed the cotton-wool from my mouth, I was able to tell him that he had pulled out the wrong tooth. Lesson49 The end of a dream 美梦告终Tired of sleeping on the floor, a young man in Teheran saved up for years to buy a real bed. For the first time in his life, he became the proud owner of a bed which had springs and a mattress. Because the weather was very hot, he carried the bed on to the roof of his house. He slept very well for the first two nights, but on the third night, a storm blew up. A gust of wind swept the bed off the roof and sent it crashing into the courtyard below. The young man did not wake up until the bed had struck the ground. Although the bed was smashed to pieces, the man was miraculously unhurt. When he woke up, he was still on the mattress. Glancing at the bits of wood and metal that lay around him, the man sadly picked up the mattress and carried it into his house. After he had put it on the floor, he promptly went to sleep again.Lesson50 Taken for a ride 乘车兜风I love travelling in the country, but I dont like losing my way. I went on an excursion recently, but my trip took me longer than I expected. Im going to Woodford Green, I said to the conductor as I got on the bus, but I dont know where it is. Ill tell you where to get off, answered the conductor. I sat in the front of the bus to get a good view of the countryside. After some time, the bus stopped. Looking round, I realized with a shock that I was the only passenger left on the bus. Youll have to get off here, the conductor said. This is as far as we go. Is this Woodford Green ? I asked. Oh dear, said the conductor suddenly. I forgot to put you off. It doesnt matter, I said. Ill get off here. We are going back now, said the conductor. Well, in that case, I prefer to stay on the bus, I answered.Lesson51 Reward for virtue 对美德的奖赏My friend, Herbert, has always been fat, but things got so bad recently that he decided to go on a diet. He began his diet a week ago. First of all, he wrote out a long list of all the foods which were forbidden. The list included most of the things Herbert loves: butter, potatoes, rice, beer, milk, chocolate, and sweets. Yesterday I paid him a visit. I rang the bell and was not surprised to see that Herbert was still as fat as ever. He led me into his room and hurriedly hid a large parcel under his desk. It was obvious that he was very embarrassed. When I asked him what he was doing, he smiled guiltily and then put the parcel on the desk. He explained that his diet was so strict that he had to reward himself occasionally. Then he showed me the contents of the parcel. It contained five large bars of chocolate and three bags of sweets! Lesson52 A pretty carpet 漂亮的地毯We have just moved into a new house and I have been working hard all morning. I have been trying to get my new room in order. This has not been easy because I own over a thousand books. To make matters worse, the room is rather small, so I have temporarily put my books on the floor. At the moment, they cover every inch of floor space and I actually have to walk on them to get in or out of the room. A short while ago, my sister helped me to carry one of my old bookcases up the stairs. She went into my room and got a big surprise when she saw all those books on the floor. This is the prettiest carpet I have ever seen, she said. She gazed at it for some time then added, You dont need bookcases at all. You can sit here in your spare time and read the carpet! Lesson53 Hot snake 触电的蛇At last firemen have put out a big forest fire in California. Since then, they have been trying to find out how the fire began. Forest fire are often caused by broken glass or by cigarette ends which people carelessly throw away. Yesterday the firemen examined the ground carefully, but were not able to find any broken glass. They were also quite sure that a cigarette end did not start the fire. This morning, however, a fireman accidentally discovered the cause. He noticed the remains of a snake which was wound round the electric wires of a 16,000-volt power line. In this way, he was able to solve the mystery. The explanation was simple but very unusual. A bird had snatched up the snake from the ground and then dropped it on to the wires. The snake then wound itself round the wires. When it did so, it sent sparks down to the ground and these immediately started a fire.Lesson54 Sticky fingers 粘糊的手指After breakfast, I sent the children to school and then I went to market. It was still early when I returned home. The children were at school, my husband was at work and the house was quiet. So I decided to make some tarts for tea. In a short time I was busy mixing butter and flour and my hands were soon covered with sticky pastry. At exactly that moment, the telephone rang. Nothing could have been more annoying. I picked up the receiver between two sticky fingers and was dismayed when I recognized the voice of Mrs Bates. It took me ten minutes to persuade her to ring back later. At last I hung up the receiver. What a mess! There was pastry on my fingers, on the telephone, and on the door-knobs. I had no sooner got back to the kitchen than the door-bell rang loud enough to wake the dead. This time it was the postman and he wanted me to sign for a registered letter !Lesson55 Not a gold mine 并非金矿Dreams of finding lost treasure almost came true recently. A new machine called The Revealer has been invented and it has been used to detect gold which has been buried in the ground. The machine was used in a cave near the seashore where-it is said-pirates used to hide gold. The pirates would often bury gold in the cave and then fail to collect it. Armed with the new machine, a search party went he did not like it. She enjoyed herself making the assistant bring almost everything in the window before finally buying the dress she had first asked for.Lesson58 A blessing in disguise? 是因祸得福吗？The tiny village of Frinley is said to possess a cursed tree. Because the tree was mentioned in a newspaper, the number of visitors to Frinley has now increased. The tree was planted near a church fifty years ago, but it is only in recent years that it has gained an evil reputation. It is said that if anyone touches the tree, he will have bad luck; if he picks a leaf, he will die. Many villagers believe that the tree has already claimed a number of victims. The vicar has been asked to have the tree cut down, but so far he has refused. He has pointed out that the tree is a useful source of income as tourists have been coming from all parts of the country to see it. In spite of all that has been said, the第1讲： 旋 转1一、填空题1 如图，AOB旋转到AOB的位置若AOA=90，则旋转中心是点_旋转角是_点A的对应点是_线段AB的对应线段是_B的对应角是_BOB=_2 如图，ABC绕着点O旋转到DEF的位置，则旋转中心是_旋转角是_AO=_，AB=_，ACB=_1题图 2题图 3题图3 如图，正三角形ABC绕其中心O至少旋转_度，可与其自身重合4 一个平行四边形ABCD，如果绕其对角线的交点O旋转，至少要旋转_度，才可与其自身重合5 钟表的运动可以看作是一种旋转现象，那么分针匀速旋转时，它的旋转中心是钟表的旋转轴的轴心，经过45分钟旋转了_度6 旋转的性质是对应点到旋转中心的_相等；对应点与旋转中心所连线段的夹角等于_；旋转前、后的图形之间的关系是_7 把一个图形绕着某一个点旋转_，如果它能够与另一个图形_，那么称这两个图形关于这个点对称或中心对称，这个点叫做_，这两个图形中的对应点叫做关于中心的_8 关于中心对称的两个图形的性质是：(1) 关于中心对称的两个图形，对称点所连_都经过_，而且被对称中心所_(2) 关于中心对称的两个图形是_9 线段不仅是轴对称图形，而且是_图形，它的对称中心是_10 平行四边形是_图形，它的对称中心是_11 圆不仅是轴对称图形，而且是_图形，它的对称中心是_12 若线段AB、CD关于点P成中心对称，则线段AB、CD的关系是_13 如图，若四边形ABCD与四边形CEFG成中心对称，则它们的对称中心是_，点A的对称点是_，E的对称点是_BD_且BD=_连结A，F的线段经过_，且被C点_，ABD_13题图 15题图14 若O点是ABCD对角线AC、BD的交点，过O点作直线l交AD于E，交BC于F则线段OF与OE的关系是_，梯形ABFE与梯形CDEF是_图形15 如图，用等腰直角三角板画AOB=45，并将三角板沿OB方向平移到如图所示的虚线处后绕点M按逆时针方向旋转22，则三角板的斜边与射线OA的夹角a为_16 如图，把边长为1的正方形ABCD绕顶点A逆时针旋转30到正方形ABCD，则它们的公共部分的面积等于_17 在平面直角坐标系中，已知点P0的坐标为(1，0)，将点P0绕着原点O按逆时针方向旋转60得到P1，延长OP1到点P2，使OP2=2OP1，再将点P2绕着原点O按逆时针方向旋转60，得点P3，则P3的坐标是_18 如图，已知梯形ABCD中，ADBC，B=90，AD=3，BC=5，AB=1，把线段CD绕点D逆时针旋转90到DE位置，连结AE，则AE的长为_16题图 18题图 19题图19 如图，以等腰直角三角形ABC的斜边AB为边作等边ABD，连结DC，以DC为边作等边DCE，B，E在C，D的同侧若则BE=_20 如图，已知D，E分别是正三角形的边BC和CA上的点，且AE=CD，AD与BE交于P，则BPD_20题图二、选择题1. 下图中，不是旋转对称图形的是( )2. 有下列四个说法，其中正确说法的个数是( )图形旋转时，位置保持不变的点只有旋转中心；图形旋转时，图形上的每一个点都绕着旋转中心旋转了相同的角度；图形旋转时，对应点与旋转中心的距离相等；图形旋转时，对应线段相等，对应角相等，图形的形状和大小都没有发生变化A1个B2个C3个D4个3. 如图，把菱形ABOC绕点O顺时针旋转得到菱形DFOE，则下列角中不是旋转角的为( )A ABOFBAODB CCOEDCOF4. 如图，若正方形DCEF旋转后能与正方形ABCD重合，则图形所在平面内可作为旋转中心的点共有( )个A1B2C3D45. 下面各图中，哪些绕一点旋转180后能与原来的图形重合?( )A、B、C、D、6. 下列图形中，不是中心对称图形的是( )A圆B菱形C矩形D等边三角形7. 以下四个图形中，既是轴对称图形又是中心对称图形的有( )A4个B3个C2个D1个8. 下列图形中，是中心对称图形的有( )A1个B2个C3个D4个9. 下列图形中，是轴对称图形而不是中心对称图形的是( )10. 下列图形中，既是中心对称图形又是轴对称图形的是( )A等边三角形B菱形C等腰梯形D平行四边形11. 数学课上，老师让同学们观察如图所示的图形，问：它绕着圆心O旋转多少度后和它自身重合?甲同学说：45；乙同学说：60；丙同学说：90；丁同学说：135以上四位同学的回答中，错误的是( )A甲B乙C丙D丁12. 如图，在平面直角坐标系中，ABC和DEF为等边三角形，AB=DE，点B，C，D在x轴上，点A，E，F在y轴上，下面判断正确的是( )A DEF是ABC绕点O顺时针旋转90得到的B DEF是ABC绕点O逆时针旋转90得到的C DEF是ABC绕点O顺时针旋转60得到的D DEF是ABC绕点O顺时针旋转120得到的13. 以下图的边缘所在直线为轴将该图案向右翻折后，再绕中心旋转180，所得到的图形是( )三、解答题14. 已知：如图，四边形ABCD及一点P求作：四边形ABCD，使得它是由四边形ABCD绕P点顺时针旋转150得到的15. 已知：如图，当半径为30cm的转动轮按顺时针方向转过120角时，传送带上的物体A向哪个方向移动?移动的距离是多少?16. 已知：如图，F是正方形ABCD中BC边上一点，延长AB到E，使得BE=BF，试用旋转的性质说明：AF=CE且AFCE17. 已知：如图，若线段CD是由线段AB经过旋转变换得到的A 求作：旋转中心O点18. 已知：如图，P为等边ABC内一点，APB=113，APC=123，试说明：以AP、BP、CP为边长可以构成一个三角形，并确定所构成三角形的各内角的度数19. 已知：如图，四边形ABCD与四边形EFGH成中心对称，试画出它们的对称中心，并简要说明理由20. 如图，有一块长方形钢板，工人师傅想把它分成面积相等的两部分，请你在图中画出作图痕迹21. 已知：三点A(1，1)，B(3，2)，C(4，1)(1) 作出与ABC关于原点对称的A1B1C1，并写出各顶点的坐标；(2) 作出与ABC关于P(1，2)点对称的A2B2C2，并写出各顶点的坐标22. 已知：直线l的解析式为y=2x3，若先作直线l关于原点的对称直线l1，再作直线l1关于y轴的对称直线l2，最后将直线l2沿y轴向上平移4个单位长度得到直线l3，试求l3的解析式23. 如图，将给出的4张扑克牌摆成第一行的样子，然后将其中的1张牌旋转180成第二行的样子，你能判断出被旋转过的1张牌是哪一张吗?为什么?四、综合题1 已知：如图，四边形ABCD中，D=60，B=30，AD=CD求证：BD2=AB2BC22 已知：如图，E是正方形ABCD的边CD上任意一点，F是边AD上的点，且FB平分ABEA 求证：BE=AFCE3 已知：如图，在四边形ABCD中，BD=180，AB=AD，E，F分别是线段BC，CD上的点，且BEFD=EF求证：4 已知：如图，RtABC中，ACB=90，D为AB中点，DE、DF分别交AC于E，交BC于F，且DEDF如果CA=CB，求证：AE2BF2=EF2；如果CACB，(1)中的结论还成立吗?若成立，请证明；若不成立，请说明理由第2讲：旋转的应用（直击中考）1、四边形ABCD中，ABC60度，ADC120度，求证：BDAD+CD2、正方形ABCD中，E为BC上的一点，F为CD上的一点，BE+DF=EF，求EAF的度数. 3、D为等腰斜边AB的中点，DMDN,DM,DN分别交BC,CA于点E,F。（1） 当绕点D转动时，求证DE=DF。（2） 若AB=2，求四边形DECF的面积。4、如图，是边长为3的等边三角形，是等腰三角形，且，以D为顶点做一个角，使其两边分别交AB于点M，交AC于点N，连接MN，则的周长为 ； 5、(2010年朝阳一模) 23（本小题满分7分）请阅读下列材料：问题：如图1，在等边三角形ABC内有一点P，且PA=2， PB=， PC=1求BPC度数的大小和等边三角形ABC的边长李明同学的思路是：将BPC绕点B顺时针旋转60，画出旋转后的图形（如图2）连接PP，可得PPC是等边三角形，而PPA又是直角三角形（由勾股定理的逆定理可证）所以APB=150，而BPC=APB=150进而求出等边ABC的边长为问题得到解决请你参考李明同学的思路，探究并解决下列问题：如图3，在正方形ABCD内有一点P，且PA=，BP=，PC=1求BPC度数的大小和正方形ABCD的边长图3图2图16、已知:PA=,PB=4,以AB为一边作正方形ABCD,使P、D两点落在直线AB的两侧.如图,当APB=45时,求AB及PD的长;7、（2009年崇文一模）25(本小题满分8分)在等边ABC的两边AB、AC所在直线上分别有两点M、N，D为ABC外一点，且MDN60，BDC120，BDCD探究：当点M、N分别在直线AB、AC上移动时，BM、NC、MN之间的数量关系及AMN的周长Q与等边ABC的周长L的关系()如图，当点M、N在边AB、AC上，且DMDN时，BM、NC、MN之间的数量关系是_；此时_；()如图，当点M、N在边AB、AC上，且当DMDN时，猜想()问的两个结论还成立吗?写出你的猜想并加以证明；()如图，当点M、N分别在边AB、CA的延长线上时，若ANx，则Q_(用x、L表示)8、（2009年崇文二模）以的两边AB、AC为腰分别向外作等腰Rt和等腰Rt，连接DE，M、N分别是BC、DE的中点探究：AM与DE的位置关系及数量关系（1）如图 当为直角三角形时，AM与DE的位置关系是 ，线段AM与DE的数量关系是 ；（2）将图中的等腰Rt绕点A沿逆时针方向旋转(090)后，如图所示，（1）问中得到的两个结论是否发生改变？并说明理由9、（2009年丰台一模）23如图1，在中，为锐角，点为射线上一点，联结，以为一边且在的右侧作正方形（1）如果，当点在线段上时（与点不重合），如图2，线段所在直线的位置关系为 _ ，线段的数量关系为 ；当点在线段的延长线上时，如图3，中的结论是否仍然成立，并说明理由；（2）如果，是锐角，点在线段上，当满足什么条件时，（点不重合），并说明理由 图1ABDFEC图2ABDECFFD图3ABDCE10、（2009中考真题）24在ABCD中，过点C作CECD交AD于点E，将线段EC绕点E逆时针旋转90得到线段EF(如图)(1)在图中画图探究：当P1为射线CD上任意一点(P1不与C点重合)时，连结EP1，将线段EP1绕点E逆时针旋转90得到线段EG1判断直线FG1与直线CD的位置关系并加以证明；当P2为线段DC的延长线上任意一点时，连结EP2，将线段EP2绕点E逆时针旋转90得到线段EG2判断直线G1G2与直线CD的位置关系，画出图形并直接写出你的结论第3讲：圆的基本概念及垂径定理一、 基础知识填空1. 由圆的定义可知：(1) 圆上的各点到圆心的距离都等于_；在一个平面内，到圆心的距离等于半径长的点都在_因此，圆是在一个平面内，所有到一个_的距离等于_的_组成的图形(2) 要确定一个圆，需要两个基本条件，一个是_，另一个是_，其中，_确定圆的位置，_确定圆的大小2. 连结_的_叫做弦经过_的_叫做直径并且直径是同一圆中_的弦3. 圆上_的部分叫做圆弧，简称_，以A，B为端点的弧记作_，读作_或_4. 圆的_的两个端点把圆分成两条弧，每_都叫做半圆5. 在一个圆中_叫做优弧；_叫做劣弧6. 半径相等的两个圆叫做_圆是_对称图形，它的对称轴是_；圆又是_对称图形，它的对称中心是_垂直于弦的直径的性质定理是_平分_的直径_于弦，并且平分_二、 填空题7. 如下图，(1)若点O为O的圆心，则线段_是圆O的半径；线段_是圆O的弦，其中最长的弦是_；_是劣弧；_是半圆(1) (2)若A=40，则ABO=_，C=_，ABC=_8. 圆的半径为5cm，圆心到弦AB的距离为4cm，则AB=_cm9. 如图，CD为O的直径，ABCD于E，DE=8cm，CE=2cm，则AB=_cm 7题 9题 10题10. 如图，O的半径OC为6cm，弦AB垂直平分OC，则AB=_cm，AOB=_11. 如图，AB为O的弦，AOB=90，AB=a，则OA=_，O点到AB的距离=_11题 12题 13题12. 如图，O的弦AB垂直于CD，E为垂足，AE=3，BE=7，且AB=CD，则圆心O到CD的距离是_13. 如图，P为O的弦AB上的点，PA=6，PB=2，O的半径为5，则OP=_14. 如图，O的弦AB垂直于AC，AB=6cm，AC=4cm，则O的半径等于_cm14题图