定语从句培优补差经典训练题(含解析)
定语从句培优补差经典训练题
一、单句改错
1.The reason why he gave for his being late for the meeting was that he got caught in traffic jam.
2I saw a car and many people who were in front of the hill.
3 There is something important about being together and sharing life what cannot be found over a telephone wire.
二、单选题
4.I was with my son about his carelessness, which the main cause of his failure in maths.
A.annoyed ; were
B.amazed ; was
C.amazing; were
D.annoyed; was
5.The old temple _____ roof was damaged in a storm is now under repair.
A.its
B.which
C.whose
D.of which
6.This is the very book ____ I want to find.
A.which
B.that
C.what
D.whom
7.Mencius believed that the reason_________man is different from animals is________man is good.
A.that; that
B.why; because
C.why; that
D.which; that
8.—Do you know _______ they got to know each other?
—It was last year_______ they both taught Chinese in Scotland.
A.when it was that, when
B.when it was that, while
C.when it was that, that
D.when it was that, as
9.It is the education _______ he received when studying abroad _______has made him such an excellent manager.
A.which, that
B.which, which
C.that, which
D.that, where
10.The school _________ I graduated is no longer what it used to be.
A.from where
B.which
C.in which
D.from which
11.Let’s think of a situation this idiom can beused.
A.that
B.which
C.as
D.where
12.---What are you talking about?
---The chemical works and its owner _______ we have just visited.
A.that
B.which
C.whom
D.what
13._______ was in that house _______ a lot of trees surround that the movie was shot.
A.It; where
B.There; where
C.It; which
D.There; which
14.I shall never forget those days ______ I spent with the earthquake victims(受害者), _____ has a great effect on my life.
A.that; which
B.when; which
C.which; that
D.when; who
15.Henry hopes to find a job ____________ his management skills can be put to good use.
A.that
B.which
C.how
D.where
16.I was born in Hangzhou, a city ____________ name will create a picture of beautiful lakes and trees in our mind.
A.which
B.of which
C.that
D.whose
17.If they continue abusing drugs, in the end drug users will find themselves trapped in a prison ________ they cannot escape.
A.to which
B.from which
C.by which
D.in which
18.—Do you have anything to say for yourselves?—Yes, there is one point________ we must insist on.
A.why
B.where
C.how
D.that
19.Young people who have got jobs may realize university lessons can’t be the only preparation for all of the situations ________ appear in the working world.
A.where
B.when
C.that
D.what
20.The moment _____ I learned the results of the competition was one of the happiest times in my life.
A.which
B.when
C.where
D.why
21.Mr. Smith was so angry at all ______ Bill was doing ______ he left.
A.that; what
B.that; that
C.which; which
D.what; that
22.The most energetic festivals are the ones _____ look forward to the coming of spring.
A.that
B.whose
C.which
D./
23.– Where did you buy your book?
– It was in the bookstore _____ I used to work.
A.that
B.where
C.when
D.which
24.I was lucky to be given an opportunity ___________ I could put what I had learned to use.
A.when
B.what
C.where
D.which
25.Moving abroad means entering a culture ______ the customs and the language are different.
A.where
B.when
C.which
D.whose
26.All of us have the desire to visit the three main temples in Athens, especially _______ contains a gold and ivory statue of Athena.
A.the one that
B.one that
C.the one
D.one
27.He is one of those people _____ everybody will find _____ hard to please.
A.that; being
B.whom; /
C.who; is
D.which; to be
28.The hotel _______ during our holidays stands by the seaside.
A.we stayed at it
B.we stayed at
C.we stayed
D.where we stayed at
三、填空题
29.Though it is 20 years since we last met, I still remember the scene in we got separated on a rainy day.
30.He wrote a letter he explained what had happened in the accident.
31.Creating an atmosphere employees feel part of a team is a big challenge.
32.This is the only way leads to your success.
33.I didn’t become a serious climber until the fifth grade,I went up to rescue a kite that was stuck in the branches of a tree.
34.The clever boy made a hole in the wall, through he could see what was going on inside the house.
35.The number of smokers, is reported,has dropped by 17 percent in just one year.
36.Great changes have taken place in that school.It is no longer it was 20 years
ago, it was poorly equipped.
37.I intended to compare notes with a friend, unfortunately couldn’t spare me even one minute.
38.In some places, red indicates sadness, as in South Africa, it is the color people wear when they mourn.
39.The settlement is home to nearly 1,000 people, many of left their village homes for a better life in the city.
40.She showed the visitors around the museum, the construction had taken more than three years.
一、单句改错
1.答案：The reason
/why that which
he gave for his being late for the meeting was that he got caught in traffic jam.
解析：
答案： I saw a car and many people were in front of the hill.
答案： There is something important about being together and sharing life
cannot be found over a telephone
wire.
二、单选题
答案： D 解析： 句意:我为儿子的粗心感到生气,这是他数学不及格的主要原因。amazed 惊讶的,annoyed 生气的,故第一空用 annoyed 。which 指的是his carelessness,故第二空应用单数。
5.答案：C
解析：
6.答案：B
解析：
7.答案：C
解析：考查定语从句和表语从句。the reason 是先行词,在定从 man is different from animals 中作原因状语,用why 引导; man is good 是表语从句,且句子不缺成分,要用that 引导。所以选C 。
8.答案：A
解析：考査强调句的特殊疑问句形式及定语从句。句意: “你知道是在什么时候他们相互认识的?”“那是在去年,他们都在苏格兰教汉语时认识的。”know 后面接一个宾语从句,故第一空应用陈述语序when it was that;第二空中last year 后面接一个定语从句,从句主干完整,故last year 在从句中作状语,使用关系副词when 。
9.答案：A
解析：
10.答案：D
解析：
11.答案：D
解析：考察定语从句。situation 在本句中表示“语境”,定语从句中缺少相应的地点状语, 故用where(或in which)来引导。故D 正确。
点评:where 引导定语从句时,是表示地点或者抽象意义“在…方面”,本身在从句部分充当地点状语。并且有些时候一些词会很抽象的用作地点,比如,case,stage,position,state,activity,business,occasion,situation,point 等,但也要视情况而定。
12.答案：A
解析：
13.答案：C
解析：
14.答案：A
解析：
16.答案：D
解析：
17.答案：B
解析：
答案： D
解析：考查定语从句:句意:——你有什么要为自己说的吗?——是,有一点是我们要坚持的。这是定语从句,先行词是point,定语从句中缺少宾语,用that或which引导定语从句,选D。
答案： C
解析：注意在本句里的situation是先行词,在空格后的定语从句里缺少的是主语,而且指的是物,所以该空我们可以用which或者that,但是不管用什么都不能省略。
20.答案：B
解析：
21.答案：B
解析：主要测试宾语从句。由句子的语境可知译文为:史密斯先生对比尔做的他让比尔做的事情如此生气。第一空主要测试定语从句,并且先行词为不定代词all,只能选择关系代词that;第二空主要测试状语从句:是so...that...句型，选B
22.答案：A
解析：
23.答案：B
解析：
24.答案：C
解析：
25.答案：A
解析：
答案： A
解析：考查定语从句。the one为先行词,从句中缺少主语,所以使用关系代词that。
答案： B
解析：句意:人们将会发现他是很难感到满意的人之一。关系代词指人,并在定语从句中作find的宾语,故用whom。宾语已提前,故后一空不填。
答案： B
三、填空题
答案：which
解析：句意为:尽管自从我们上次见面已经有20年了,我仍然记得我们在下雨天分离的场景.定语从句修饰先行词scene，再根据设空前的in可知填which
答案：where/in which
解析：句意:他写了一封信,信中他解释了事故中发生了什么。本题考查定语从句。从空格处到句尾是定语从句,修饰先行词letter。将先行词代入从句后为: He explained what had happened in the accident in the letter.由此可知从句中缺少状语,应该用关系副词where或in which。
答案：in which/where
解析：句意:创造一种雇员感觉自己是团队一部分的氛围是很大的挑战。先行词是atmosphere,从句缺少状语,可以用关系副词where,也可根据先行词构成"in an atmosphere ”搭配,故也可用"in which”引导定语从句。
答案：that
答案：when
解析：句意:我直到五年级才真正成为一个攀登者,那时,我爬到树上去拿一个被挂在树枝上的风筝。考查定语从句。先行词为the fifth grade,设空处在定语从句中作时间状语,故用when。
解析：句意:就像报道的那样,吸烟者数量在一年内下降了17%。考查定语从句。as在此处引导非限制性定语从句,表示“正如……”。
答案：what; when
答案：who
答案：where
解析：句意:在一些地方,红色代表着悲哀,正如在南非,在那里红色是哀悼的时候人们所穿的衣服的颜色。考查非限制性定语从句。分析句子结构可知,先行词是South Africa,从句中缺少地点状语,故用关系副词where。
答案：whom
解析：句意:这个居民区住了将近1,000人,其中很多是离开他们的家乡来城市追求更好的生活。考查非限制性定语从句。“不定代词/数词+of whom(指人)/which(指物)”为非限制性定语从句用法,表示“整体中的一部分”,由于前面先行词指人,故填whom。
答案：of which
解析：句意:她带领参观者参观了这个博物馆,其建造花费了三年多的时间。考查非限制性定语从句。the con struction与which代替的the museum之间为所属关系,故用of which。
最新英语定语从句专题训练答案 一、定语从句 1． ---Our English teacher is very kind, and we all like her very much. ---That’s for sure. A person _________ cares for others is popular everywhere. A． who B． which C． whom D． whose 【答案】A 【解析】 试题分析：句意：--我们的英语老师非常的善良，并且我们非常喜欢她。--那是当然。一个关心他人的人到处都受到欢迎。根据先行词是person,所以引导词用that 或者who。结合选项，故选A。 考点：考查定语从句的用法。 2．Linda will never forget the words her father told her. A．that B．who C．where D．what 【答案】A 【解析】 【详解】 句意：Linda将永远不会忘记她父亲告诉她的这些话。that关系代词，引导定语从句，先行词可以为人或物；who关系代词，引导定语从句，先行词为人；where是关系副词，引导定语从句，在从句中作地点状语；what什么，常引导名词性从句，不能引导定语从句。根据句子结构可知，这里是一个定语从句，修饰空前的the words，指物，且在从句中作宾语，故应选A。 3．The girl handed everything _____ she had picked up in the street to the police. A．which B．in which C．that D．all 【答案】C 【解析】 【详解】 句意：女孩把她在街上捡到的所有东西都交给了警察。 考查定语从句。本句先行词everything是不定代词，应该用关系代词that引导此定语从句。故选C。 4．Yesterday, Mr. Green went to his hometown and visited the old house ____ he was born in. A．which B．where C．what D．it 【答案】A 【解析】 试题分析：句意：昨天，格林先生去了他的家乡并且参观了他出生时的那所旧房子。____ he was born in是定语从句，修饰house。先行词是house，关系代词词用that或者which，
E D F C B A 三角形培优训练专题 【三角形辅助线做法】 图中有角平分线，可向两边作垂线。也可将图对折看，对称以后关系现。 角平分线平行线，等腰三角形来添。角平分线加垂线，三线合一试试看。 线段垂直平分线，常向两端把线连。要证线段倍与半，延长缩短可试验。 三角形中两中点，连接则成中位线。三角形中有中线，延长中线等中线。 【常见辅助线的作法有以下几种】 1、遇到等腰三角形，可作底边上的高，利用“三线合一”的性质解题，思维模式是全等变换中的“对折”。 2、遇到三角形的中线，倍长中线，使延长线段与原中线长相等，构造全等三角形，利用的思维模式是全等变换中的“旋转”。 3、遇到角平分线，可以自角平分线上的某一点向角的两边作垂线，利用的思维模式是三角形全等变换中的“对折”，所考知识点常常是角平分线的性质定理或逆定理。 4、过图形上某一点作特定的平分线，构造全等三角形，利用的思维模式是全等变换中的“平移”或“翻转折叠”。 5、截长法与补短法，具体做法是在某条线段上截取一条线段与特定线段相等，或是将某条线段延长，是之与特定线段相等，再利用三角形全等的有关性质加以说明。这种作法，适合于证明线段的和、差、倍、分等类的题目。 6、已知某线段的垂直平分线，那么可以在垂直平分线上的某点向该线段的两个端点作连线，出一对全等三角形。 7、特殊方法：在求有关三角形的定值一类的问题时，常把某点到原三角形各顶点的线段连接起来，利用三角形面积的知识解答。 1、已知，如图△ABC中，AB=5，AC=3，求中线AD的取值范围. 2、如图，△ABC中，E、F分别在AB、AC上，DE⊥DF，D是中点，试比较BE+CF与EF的大小.
初中英语定语从句专题训练答案 一、定语从句 1．–Why are you so worried? -I’ve lost the watch ______ my dad bought me on my birthday. A．what B．who C．whose D．which 【答案】D 【解析】 【分析】 【详解】 句意：——你为什么如此担心？——我把那块我生日时爸爸买给我的手表弄丢了。考查定语从句，先行词是watch表示物，故关系代词只能用which或that；what不引导定语从句；who的先行词是人；whose表示所属；故选D。 2．I will never forget the fire ______________ happened in Shanghai last year. A．when B．where C．what D．which 【答案】D 【解析】 【分析】 考点：考查定语从句。 【详解】 试题分析：句意：我将永远不会忘记去年上海发生的火灾。先行词the fire是物，故其定语从句要用which引导。what不引导定语从句；when先行词是时间；where先行词是地点；根据题意，故选D。 3．–What are you looking for? –I’m looking for the storybook you lent to me last week. A．who B．which C．when 【答案】B 【解析】 【详解】 句意“-你正在找什么？-我正在找你上周借给我的故事书”。 本题考查定语从句。A.who指人，在从句中作主语和宾语；B.which指物，在从句中作主语和宾语；C.when表示时间，在从句中作状语。本句话中，先行词为the storybook，指物，且在从句中作宾语，故选B。
全等三角形证明题专练 1、已知，如图，AB ⊥AC ，AB ＝AC ，AD ⊥AE ，AD ＝AE 。求证：BE ＝CD 。 2、已知：如图，AB ⊥BC ，AD ⊥DC ，AB=AD ，若E 是AC 上一点。求证：EB=ED 。 D A E C B 3、已知：如图，AB 、CD 交于O 点，CE//DF ，CE=DF ，AE=BF 。求证：∠ACE=∠BDF 。 A E D C B A B C D E F O
4、如图，△ABC 中，AB=AC ，过A 作GE ∥BC ，角平分线BD 、CF 交于点H ，它们的延长线分别交GE 于E 、G ，试在图中找出三对全等三角形，并对其中一对给出证明。 5、如图，在△ＡＢＣ中，点Ｄ在ＡＢ上，点Ｅ在ＢＣ上，ＢＤ＝ＢＥ。 （１） 请你再添加一个条件，使得△ＢＥＡ≌△ＢＤＣ，并给出证明。 你添加的条件是：________ ___ （2）根据你添加的条件，再写出图中的一对全等三角形： ______________（不再添加其他线段，不再标注或使用 其他字母，不必写出证明过程） 6、已知：如图，△ABC 中，AD ⊥BC 于D ，E 是AD 上一点，BE 的延长线交AC 于F ，若BD=AD ，DE=DC 。求证：BF ⊥AC 。 F E D C A B G H A B C D E F
7、已知：如图，△ABC 和△A ＇B ＇C ＇中，∠BAC=∠B ＇A ＇C ＇，∠B=∠B ＇，AD 、A ＇D ＇分别是∠BAC 、∠B ＇A ＇C ＇的平分线，且AD=A ＇D ＇。求证：△ABC ≌△A’B’C’。 8、已知：如图，AB=CD ，AD=BC ，O 是AC 中点，OE ⊥AB 于E ，OF ⊥CD 于F 。求证：OE=OF 。 A B C D E F O 9、已知：如图，AC ⊥OB ，BD ⊥OA ，AC 与BD 交于E 点，若OA=OB ，求证：AE=BE 。 O B A C D E A B C D A' B' C' D' 1 2 3 4
定语从句专项练习题及详解50题 1.The place _______interested me most was the Children's Palace. A. Which B. where C. what D. in which 2.Do you know the man _______? A. whom I spoke B. to who spoke C. I spoke to D. that I spoke 3.This is the hotel _______last month. A. which they stayed B. at that they stayed C. where they stayed at D. where they stayed 4.Do you know the year ______the Chinese Communist Party was founded? A. which B. that C. when D. on which 5.That is the day ______I'll never forget. A. which B. on which C. in which D. when 6.The factory ______we'll visit next week is not far from here. A. where B. to which C. which D. in which 7.Great changes have taken place since then in the factory _______we are working. A. where B. that C. which D. there 8.This is one of the best films _______. A. that have been shown this year B. that have shown C. that has been shown this year D. that you talked 9.Can you lend me the book ______the other day? A. about which you talked B. which you talked C. about that you talked D. that you talked 10.The pen ______he is writing is mine. A. with which B. in which C. on which D. by which 11.They arrived at a farmhouse, in front of ______sat a small boy. A. whom B. who C. which D. that 12.The engineer ______my father works is about 50 years old. A. to whom B. on whom C. with which D. with whom 13.It there anyone in your class ______family is in the country? A. who B. who's C. which D. whose 14.I'm interested in ______you have said. A. all that B. all what C. that D. which 15.I want to use the same dictionary ______was used yesterday. A. which B. who C. what D. as 16.He isn't such a man ______he used to be. A. who B. whom C. that D. as 17.He is good at English, ______we all know. A. that B. as C. whom D. what 18.Li Ming, ______to the concert enjoyed it very much. A. I went with B. with whom I went C. with who I went D.I went with him 19.I don't like ______ as you read. A. the novels B. the such novels C. such novels D. same novels 20.He talked a lot about things and persons ________they remembered in the school. A. which B. that C. whom D. what 21.The letter is from my sister, ______is working in Beijing. A. which B. that C. whom D. who
全等三角形辅助线 找全等三角形的方法： （1）可以从结论出发，看要证明相等的两条线段（或角）分别在哪两个可能全等的三角形中；（2）可以从已知条件出发，看已知条件可以确定哪两个三角形相等； （3）从条件和结论综合考虑，看它们能一同确定哪两个三角形全等； （4）若上述方法均不行，可考虑添加辅助线，构造全等三角形。 三角形中常见辅助线的作法： ①延长中线构造全等三角形； ②利用翻折，构造全等三角形； ③引平行线构造全等三角形； ④作连线构造等腰三角形。 常见辅助线的作法有以下几种： 1)遇到等腰三角形，可作底边上的高，利用“三线合一”的性质解题，思维模式是全等变换 中的“对折”． 2)遇到三角形的中线，倍长中线，使延长线段与原中线长相等，构造全等三角形，利用的思 维模式是全等变换中的“旋转”． 3)遇到角平分线，可以自角平分线上的某一点向角的两边作垂线，利用的思维模式是三角形 全等变换中的“对折”，所考知识点常常是角平分线的性质定理或逆定理． 4)过图形上某一点作特定的平分线，构造全等三角形，利用的思维模式是全等变换中的“平 移”或“翻转折叠” 5)截长法与补短法，具体做法是在某条线段上截取一条线段与特定线段相等，或是将某条线 段延长，是之与特定线段相等，再利用三角形全等的有关性质加以说明．这种作法，适合于证明线段的和、差、倍、分等类的题目． 6)特殊方法：在求有关三角形的定值一类的问题时，常把某点到原三角形各顶点的线段连接 起来，利用三角形面积的知识解答． 常见辅助线写法： ⑴过点A作BC的平行线AF交DE于F ⑵过点A作BC的垂线，垂足为D ⑶延长AB至C，使BC＝AC ⑷在AB上截取AC，使AC＝DE ⑸作∠ABC的平分线，交AC于D ⑹取AB中点C，连接CD交EF于G点
初中英语定语从句专项训练及答案及解析 一、定语从句 1．According to the survey, women ________drink more than two cups of coffee a day have a greater chance of having heart disease than ________who don’t. A． who； that B． /； these C． who； those D． / ； / 【答案】C 【解析】 试题分析：句意为：据调查，每天喝超过两杯咖啡的女人比那些不喝咖啡的女人患心脏疾病的机会大得多。根据语境可知，本题考查的是定语从句的引导词和代词的用法。在定语从句中，引导词由先行词而定，who的先行词指人。此外，这里指的是“喝咖啡与不喝咖啡的那些女人”的比较，代词应用those，表示同名同物，故应选C。 考点：考查引导词和指示代词的用法。 2．The leaders from eight countries attended the Shanghai cooperation organization summit in Qingdao got the welcome of the Chinese people. A．whom B．what C．who D．which 【答案】C 【解析】 【详解】 句意：出席上海合作组织青岛峰会的8国领导人受到中国人民的欢迎。考查关系代词辨析。what不是关系词，可排除。whom和who都用于先行词是人时，但whom用作宾语，who用作主语或宾语；which用于先行词是物时。本句先行词The leaders是人，可排除which；关系词在从句中做主语，可排除whom。根据句意结构和语境，可知选C。 3．Ant Forest is a popular mobile app_____ allows people to plant real trees in the desert by collecting “green energy points’’. A．what B．who C．whom D．which 【答案】D 【解析】 【详解】 蚂蚁森林是一款允许人们通过收集绿色能量在沙漠里种植真的树木的流行的手机应用软件。 考查定语从句。本句为定语从句，先行词是a popular mobile app指物，关系词用which，故选D。 4．The only language ____ is easy to learn is mother tongue． A．which B．that C．/ D．it 【答案】B
1 、如图，三角形ABC 内任一点P ，连接PA 、PB 、PC ， 求证：1/2（AB+BC+AC ）
8、如图，△ABC 中，AD 是高，AE ，BF 是角平分线，它们相交于点O ，∠CAB ＝50°，∠ C ＝60°，求∠DAC 及∠BOA ． 9．观察并探求下列各问题，写出你所观察得到的结论，并说明理由。 （1）如图①，△ABC 中，P 为边BC 上一点，试观察比较BP + PC 与AB + AC 的大小，并 说明理由。 C B A P 图① （2）将（1）中点P 移至△ABC 内，得图②，试观察比较△BPC 的周长与△ABC 的周长的大小，并说明理由。 C B A P 图② （3）将（2）中点P 变为两个点P 1、P 2得图③，试观察比较四边形BP 1P 2C 的周长与△ABC 的周长的大小，并说明理由。 C B A P 1P 2 图③ （4）将（3）中的点P 1、P 2移至△ABC 外，并使点P 1、P 2与点A 在边BC 的异侧，且∠P 1BC ＜∠ABC ，∠P 2CB ＜∠ACB ，得图④，试观察比较四边形BP 1P 2C 的周长与△ABC 的周长的大小，并说明理由。 图④ C B A P 1P 2
) 【定语从句专项练习】 1. Last month, part of Southeast Asia was struck by floods, from _____ effects the people are still suffering. A. that B. whose C. those D. what 2. Mark was a student at this university from 1999 to 2003, __________ he studied very hard and was made Chairman of the Students’ Union. A. during which time B. for which time C. during whose time D. by that time 3. I work in a business ______ almost everyone is waiting for a great chance. A. how B. which C. where D. that ; 4. The English play ________ my students acted at the New Year’s party was a great success. A. for which B. at which C. in which D. on which 5. New York, ________ I visited last year, is a nice old city. A. that B. which C. when D. in which 6. I can think of many cases _______students obviously knew a lot of English words and expressions but couldn't write a good essay. A. why B. which C. as D. where 7. George Orwell, ________ was Eric Arthur, wrote many political novels and essays. A. the real name B. what his real name 。
3：在直角三角形中，如果一个锐角等于 30°,那么它所对的直角边等于斜边的一 2. 定理及其推论的作用。 等腰三角形的判定定理揭示了三角形中角与边的转化关系, 理，也是把三角形中角的相等关系转化为边的相等关系的重要依据，是本节的重点。 3. 等腰三角形中常用的辅助线 等腰三角形顶角平分线、底边上的高、底边上的中线常常作为解决有关等腰三角形问 【知识精读】 （-）等腰三角形的性质 1.有关定理及其推论 定理：等腰三角形有两边相等; 3等腰三角形 定理：等腰三角形的两个底角相等（简写成“等边对等角”）。 推论1：等腰三角形顶角的平分线平分底边并且垂直于底边，这就是说，等腰三角形的 顶角平分线、底边上的中线、底边上的高互相重合。等腰三角形是以底边的垂直平分线为对 称轴的轴对称图形; 推论2:等边三角形的各角都相等，并且每一个角都等于 60 2.定理及其推论的作用 等腰三角形的性质定理揭示了三角形中边相等与角相等之间的关系, 由两边相等推出两 角相等，是今后证明两角相等常用的依据之一。等腰三角形底边上的中线、 底边上的高、顶 角的平分线“三线合一”的性质是今后证明两条线段相等， 两个角相等以及两条直线互相垂 直的重要依据。 （二）等腰三角形的判定 1.有关的定理及其推论 定理：如果一个三角形有两个角相等，那么这两个角所对的边也相等（简写成 “等角 对 等边”。） 推论 1:三个角都相等的三角形是等边三角形。 推论 2:有一个角等于60°的等腰三角形是等边三角形。 推论 它是证明线段相等的重要定
题的辅助线，由于这条线可以把顶角和底边折半，所以常通过它来证明线段或角的倍分问题, 在等腰三角形中，虽然顶角的平分线、底边上的高、底边上的中线互相重合， 添加辅助线时, 有时作哪条线都可以，有时需要作顶角的平分线，有时则需要作高或中线，这要视具体情况 来定。 【分类解析】 例1.如图，已知在等边三角形 ABC 中，D 是AC 的中点，E 为BC 延长线上一点，且CE =CD ，DM 丄BC ,垂足为M 。求证：M 是BE 的中点。 所以/ 1 = - / ABC 2 又因为CE = CD ，所以/ CDE = / E 所以/ ACB = 2/ E 即/ 1=/ E 所以BD = BE ,又DM 丄BC ,垂足为 M 分析：欲证M 是BE 的中点，已知 DM 丄BC ,所以想到连结 BD ，证BD = ED 。因为△ ABC 是等边三角形，/ DBE = - / ABC ，而由 CE = CD ，又可证/ E = - / ACB ，所以/ 1 2 2 =/ E ,从而问题得证。 证明：因为三角形 ABC 是等边三角形，D 是AC 的中点 所以M 是BE 的中点 （等腰三角形三线合一定理） 例2.如图，已知: ABC 中，AB AC , D 是 BC 上一点，且 AD DB , DC CA , 求 BAC 的度数。 E D
初中英语定语从句专项练习题与答案详解(第2套) 1.The place _______interested me most was the Children's Palace. A. Which B. where C. what D. in which 2.Do you know the man _______? A. whom I spoke B. to who spoke C. I spoke to D. that I spoke 3.This is the hotel _______last month. A. which they stayed B. at that they stayed C. where they stayed at D. where they stayed 4.Do you know the year ______the Chinese Communist Party was founded? A. which B. that C. when D. on which 5.That is the day ______I'll never forget. A. which B. on which C. in which D. when 6.The factory ______we'll visit next week is not far from here. A. where B. to which C. which D. in which 7.Great changes have taken place since then in the factory _______we are working. A. where B. that C. which D. there 8.This is one of the best films _______. A. that have been shown this year B. that have shown C. that has been shown this year D. that you talked 9.Can you lend me the book ______the other day? A. about which you talked B. which you talked C. about that you talked D. that you talked 10.The pen ______he is writing is mine. A. with which B. in which C. on which D. by which 11.They arrived at a farmhouse, in front of ______sat a small boy. A. whom B. who C. which D. that 12.The engineer ______my father works is about 50 years old. A. to whom B. on whom C. with which D. with whom 13.It there anyone in your class ______family is in the country? A. who B. who's C. which D. whose 14.I'm interested in ______you have said. A. all that B. all what C. that D. which 15.I want to use the same dictionary ______was used yesterday. A. which B. who C. what D. as 16.He isn't such a man ______he used to be. A. who B. whom C. that D. as 17.He is good at English, ______we all know. A. that B. as C. whom D. what 18.Li Ming, ______to the concert enjoyed it very much. A. I went with B. with whom I went C. with who I went D.I went with h im
全等三角形培优经典题
全等三角形培优习题 1、已知正方形ABCD中，E为对角线BD上一点，过E点作EF⊥BD交BC于F，连接DF，G为DF中点，连接EG，CG． （1）直接写出线段EG与CG的数量关系； （2）将图1中△BEF绕B点逆时针旋转45o，如图2所示，取DF中点G，连接EG，CG． 你在（1）中得到的结论是否发生变化？写出你的猜想并加以证明． （3）将图1中△BEF绕B点旋转任意角度，如图3所示，再连接相应的线段，问（1）中的结论是否仍然成立？ A D E G 图1 F A D C G 图2 F A E 图3 D
2、数学课上，张老师出示了问题：如图1，四边形ABCD 是正方形，点E是边BC的中点．90 AEF ∠=o，且EF交正方 形外角DCG ∠的平行线CF于点F，求证：AE=EF．经过思考，小明展示了一种正确的解题思路：取AB的 中点M，连接ME，则AM=EC，易证AME ECF △≌△，所以AE EF =．在此基础上，同学们作了进一步的研究： （1）小颖提出：如图2，如果把“点E是边BC的中点”改为“点E是边BC上（除B，C外）的任意一点”，其它条件不变，那么结论“AE=EF”仍然成立，你认为小颖的观点正确吗？如果正确，写出证明过程；如果不正确，请说明理由； （2）小华提出：如图3，点E是BC的延长线上（除C 点外）的任意一点，其他条件不变，结论“AE=EF”仍然成立．你认为小华的观点正确吗？如果正确，写出证明过程；如果不正确，请说明理由． A D F C G E 图A D F C G E 图 A D F C G E B 图
英语定语从句专项训练100(附答案) 一、定语从句 1．–Why are you so worried? -I’ve lost the watch ______ my dad bought me on my birthday. A．what B．who C．whose D．which 【答案】D 【解析】 【分析】 【详解】 句意：——你为什么如此担心？——我把那块我生日时爸爸买给我的手表弄丢了。考查定语从句，先行词是watch表示物，故关系代词只能用which或that；what不引导定语从句；who的先行词是人；whose表示所属；故选D。 2．That was his first invention. It was a machine ________ clothes. A．that used to wash B．which was used to washing C．which got used to washing D．that was used to wash 【答案】D 【解析】 【详解】 句意：那是他的第一个发明。那是一台用来洗衣服的机器。本题考查的是be used to do sth. “被用于做某事”的用法，而不是be/get used to doing sth. “习惯于做某事”的用法，排除 B/C；再由That was his first invention.可知，本题是过去时，因此在that引导的定语从句中，应该用一般过去时的被动句。was used to wash被用来洗衣服，语境是：那是一台被用来洗衣服的机器。故选D。 3．The leaders from eight countries attended the Shanghai cooperation organization summit in Qingdao got the welcome of the Chinese people. A．whom B．what C．who D．which 【答案】C 【解析】 【详解】 句意：出席上海合作组织青岛峰会的8国领导人受到中国人民的欢迎。考查关系代词辨析。what不是关系词，可排除。whom和who都用于先行词是人时，但whom用作宾语，who用作主语或宾语；which用于先行词是物时。本句先行词The leaders是人，可排除which；关系词在从句中做主语，可排除whom。根据句意结构和语境，可知选C。 4．– Do you like the weekly talk show The Readers on CCTV? –Sure. It’s a great TV program can develop the habit of reading.
最新初中英语定语从句专项训练及答案 一、定语从句 1．Paul’s uncle is the man taught us Chinese last year. A．where B．which C．who 【答案】C 【解析】 试题分析：句意：保罗的叔叔是那个去年教我们中文的人。本题考查定语从句的用法，根据先行词是人，可知关系词用who。故选C。 考点：考查定语从句的关系词。 2．一Which song do you like better．Maria？ 一I prefer the song Manual of Youth ______ is sung by TFBOYS． A．who B．whom C．which D．/ 【答案】C 【解析】 【详解】 C 考查定语从句的引导词。句意：—Maria，你更喜欢哪首歌？—我喜欢TFBOYS唱的《青春修炼手册》。分析句子结构，本句中的 is sung by TFBOYS在复合句中作定语从句，其中先行词 the song Manual of Youth 指物，且在定语从句中作逻辑主语，所以关系代词用which．故选C． 【点睛】 完成定于从句的关键是分析先行词指人还是指物，以及其在定语从句中做什么句子成分． 3．The old town has narrow streets and small houses _____are built close to each other. A．who B．that C．what D．They 【答案】B 【解析】 试题分析：句中先行词为small houses，在定语从句中作主语，故用关系代词that。句意：老镇有狭窄的街道，小房子建得彼此相靠近。 考点：考查定语从句的用法 4．This is the dictionary ________ Mum gave me for my birthday. A．which B．what C．whose D．whom 【答案】A 【解析】 【详解】 句意：这是那本母亲给我作为生日礼物的字典。这里是定语从句，先行词是为物时用
等腰三角形培优提高试题
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一．选择题（共6小题） 1．已知，等腰三角形的一条边长等于6，另一条边长等于3，则此等腰三角形的周长是（）A．9 B．12 C．15 D．12或15 2．如图所示，在△ABC中，AB=AC，∠A=36°，BD、CE分别为∠ABC与∠ACB的角平分线且相交于点F，则图中的等腰三角形有（） A．6个B．7个C．8个D．9个 （第2题）（第3题）（第4题） 3．如图，直线a、b相交于点O，∠1=50°，点A在直线a上，直线b上存在点B，使以点O、 A、B为顶点的三角形是等腰三角形，这样的B点有（） A．1个B．2个C．3个D．4个 4．如图，△ABC的面积为8cm2，AP垂直∠B的平分线BP于P，则△PBC的面积为（）A．3cm2B．4cm2C．5cm2D．6cm2 5．在等腰△ABC中，AB=AC，中线BD将这个三角形的周长分为15和12两个部分，则这个等腰三角形的底边长为（） A．7 B．11 C．7或11 D．7或10 6．如图：D，E分别是△ABC的边BC、AC上的点，若AB=AC，AD=AE，则（） A．当∠B为定值时，∠CDE为定值B．当∠α为定值时，∠CDE为定值 C．当∠β为定值时，∠CDE为定值D．当∠γ为定值时，∠CDE为定值 二．填空题（共8小题） 7．已知等腰三角形一腰上的中线将三角形周长分成2：1两部分，已知三角形底边长为5cm，
则腰长为cm． 8．如图，在△ABC中，EG∥BC，BF平分∠ABC，CF平分∠ACB，AB=10，AC=12，△AEG的周长为． （第8题）（第9题）（第10题） 9．如图，已知△ABC中，AB=AC，D是BC上一点，且AD=DB，DC=CA，则∠BAC=°．10．如图，△ABC中，AP垂直∠ABC的平分线BP于点P．若△ABC的面积为32cm2，BP=6cm，且△APB的面积是△APC的面积的3倍．则AP=cm． 11．等腰三角形一腰上的高与另一腰的夹角为48°，则该等腰三角形的底角的度数为．12．如图是由9个等边三角形拼成的六边形，若已知中间的小等边三角形的边长是2，则六边形的周长是． （第12题）（第14题）（第14题） 13．如图，∠AOB=60°，C是BO延长线上的一点，OC=10cm，动点P从点C出发沿CB以2cm/s 的速度移动，动点Q从点O发沿OA以1cm/s的速度移动，如果点P、Q同时出发，用t （s）表示移动的时间，当t=时，△POQ是等腰三角形． 14．如图：已知在Rt△ABC中，∠C=90°，∠A=30°，在直线AC上找点P，使△ABP是等腰三角形，则∠APB的度数为． 三．解答题（共15小题） 15．如图，已知AB=AC=AD，且AD∥BC，求证：∠C=2∠D．
最新英语定语从句专项训练100(附答案) 一、定语从句 1．（河南省2015年中考英语试题）—Why don’t you like fishing? —Fishing is a hobby needs much patience, but I’m not patient at all. A．who B．that C．it D．what 【答案】B 【解析】 【详解】 句意：——你为什么不喜欢钓鱼？——钓鱼的爱好需要很大的耐心，但我根本没有耐心。考查定语从句的用法。who谁；that那；it它；what什么。先行词a hobby是物，在定语从句中作主语，可知用关系代词that或which引导此定语从句，结合选项可知选B。 2．The leaders from eight countries attended the Shanghai cooperation organization summit in Qingdao got the welcome of the Chinese people. A．whom B．what C．who D．which 【答案】C 【解析】 【详解】 句意：出席上海合作组织青岛峰会的8国领导人受到中国人民的欢迎。考查关系代词辨析。what不是关系词，可排除。whom和who都用于先行词是人时，但whom用作宾语，who用作主语或宾语；which用于先行词是物时。本句先行词The leaders是人，可排除which；关系词在从句中做主语，可排除whom。根据句意结构和语境，可知选C。 3．When we speak of culture, we mean a way of life_________ a group of people have in common. A．what B．who C．where D．that 【答案】D 【解析】 【详解】 句意：当我们说起文化的时候，我们指的是一群人共同拥有的生活方式。考查定语从句的引导词。根据句意：当我们说起文化的时候，我们指的是一群人共同拥有的生活方式。逗号后面的句中是含有定语从句的复合句，先行词是 life，表示“物”，用引导词 that，在从句中做宾语。what 不能引导定语从句。先行词是“人”，引导词常用 who。where 在定语从句中做地点状语。故选D。 【点睛】 引导定语从句的关联词包括关系代词和关系副词。关系代词有that, which, whose, who, whom, as；关系副词有when, where, why。关系代词和关系副词在定语从句中都充当一定的句法成份。关系代词在从句中充当动词的宾语时一般可以省略。
三角形培优训练专题 【三角形辅助线做法】 图中有角平分线，可向两边作垂线。也可将图对折看，对称以后关系现。 角平分线平行线，等腰三角形来添。角平分线加垂线，三线合一试试看。 线段垂直平分线，常向两端把线连。要证线段倍与半，延长缩短可试验。 三角形中两中点，连接则成中位线。三角形中有中线，延长中线等中线。 【常见辅助线的作法有以下几种】 1、遇到等腰三角形，可作底边上的高，利用“三线合一”的性质解题，思维模式是全等变 换中的“对折” 。 2、遇到三角形的中线，倍长中线，使延长线段与原中线长相等，构造全等三角形，利用的 思维模式是全等变换中的“旋转” 。 3、遇到角平分线，可以自角平分线上的某一点向角的两边作垂线，利用的思维模式是三角 形全等变换中的“对折” ，所考知识点常常是角平分线的性质定理或逆定理。 4、过图形上某一点作特定的平分线，构造全等三角形，利用的思维模式是全等变换中的“平移” 或“翻转折叠” 。 5、截长法与补短法，具体做法是在某条线段上截取一条线段与特定线段相等，或是将某条 线段延长，是之与特定线段相等，再利用三角形全等的有关性质加以说明。这种作法，适合于证 明线段的和、差、倍、分等类的题目。 6、已知某线段的垂直平分线，那么可以在垂直平分线上的某点向该线段的两个端点作连 线，出一对全等三角形。 7、特殊方法：在求有关三角形的定值一类的问题时，常把某点到原三角形各顶点的线段连 接起来，利用三角形面积的知识解答。 1、已知，如图△ ABC 中， AB=5， AC=3，求中线 AD 的取值范围 . 2、如图，△ ABC中， E、 F 分别在 AB、 AC 上， DE⊥ DF， D 是中点，试比较BE+CF与 EF的大小 . A E F B D C