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写英语故事 英语故事短文

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篇一:《英语故事》

A Rabbit and a Wolf

A little rabbit is picking mushrooms in a forest. A wolf is coming. He is very hungry. ―Oh, a little rabbit! This is my favourite food!‖

The rabbit sees the wolf, but she is not afraid. She pretends to be poisoned by the mushrooms. The wolf thinks, ―If I eat her, I will be poisoned, too.‖ So he goes away.

Then the rabbit is very happy. She goes on picking the mushrooms.

mushroom n. 蘑菇

afraid adj. 害怕的

pretend v. 假装

poison v. 毒害

go on 继续

根据上文填空完成下面各题。

1. The wolf is ______. He wants to _________ the rabbit.

2. The rabbit is not __________.

3. She pretends to be ______.

译文:

兔子和狼

一只小兔子正在森林里采蘑菇,一只狼来了,他很饿。―哦,一只小兔子!这是我最喜欢的食物!‖

小兔子看见了狼,但是她并不害怕。她假装吃蘑菇中毒了。狼想到:―如果我吃了她,我也会中毒的。‖所以他走开了。

小兔子非常高兴,她继续去采蘑菇。

参考答案:

1. hungry, eat

2. afraid

3. poisoned

A Foolish Man

A man in ancient times thought he was clever, but he always did foolish things.

One day, he saw a beautiful bell. It was at the top of a door. ―Oh, how nice! I will take it home. ‖he said to himself. He thought hard. Then he had a ―good‖ idea. ―Aha! I can plug my ears. I will not hear the ring.‖

He did so, but the bell rang. The owner opened the door and asked angrily, ―What are you doing here?‖ foolish adj. 傻的,愚蠢的

while conj. 当…的时候

owner n. 主人

top n. 顶部

cover v. 盖上

ancient adj. 古代的

angrily adv. 生气的

plug v. 堵,塞

根据上文,回答下面的问题。

1. What did the man want to do with the bell?

2. Did the owner discover (发现) it?

3. Was the man‘s idea good?

译文:

一个愚蠢的人

古时候,有一个以为自己很聪明,但是他总是干傻事。

有一天,他看见一个漂亮的铃铛挂在一户人家的门上头。―啊,好漂亮!我要把它拿回家去。‖他自言自语道。他使劲地想,然后想到了一个―好‖主意。―哈!我把耳朵堵上,就听不到铃声了。‖

他这样做了,但是铃铛响了起来。主人打开门,生气地问道:―你在这儿干什么?‖

参考答案:

1. He wanted to take it home.

2. Yes, he did.

3. No, it wasn‘t.

A clever Old Man

Sam is an old man. He likes walking in the street after supper. And he goes home at seven o‘clock.{写英语故事}.

But a car stops at his house tonight. A policeman helps him get out. Then he tells Sam‘s wife, ―The old man got lost in the street. He asked me to take him home in the car.‖

After the policeman leaves, his wife asks, ―Sam, you go to that street every night. How can you get lost?‖ ―I am not lost. I just don‘t want to go home on foot.‖ Sam answers.

tonight n. 今晚,今夜

get lost = be lost 迷路

leave v. 离开

on foot 步行

根据上文,判断下面各题的对与错,正确的写―F‖,错误的写―T‖。

1. Sam likes walking in the street after lunch. ( )

2. Sam does something wrongly, so the policeman comes. ( )

3. He is not lost. ( )

4. He doesn‘t want to walk home tonight. ( )

译文:

一个聪明的老人

萨姆是一个老人。他喜欢在晚饭后到大街上散步,然后7点钟回家。

但是,今天晚上一辆小汽车停在他家门前。一名警察帮助他下了车,然后他告诉萨姆的妻子:―这位老人在街上迷路了。他让我用汽车送他回来。‖

警察离开后,他妻子问道:―萨姆,你每天晚上都去那条街,你怎么会迷路呢?‖

―我没有迷路。我只是不想走路回家。‖萨姆回答道。

参考答案:

1. F 2. F 3. T 4. T

A Cat Is Fishing

A cat goes to a river every day. He wants to go fishing. But he can‘t catch any fish.

One day, he goes to the river as usual. Suddenly a fish comes out. He catches the fish. He is very happy. He forgets to put the fish in the basket. He dances and sings. He shouts, ―I have a fish! I have a fish!‖ All his friends come to see him.

―Where is your fish? Let us have a look at it. ‖ his friends say.

―It‘s there, near the bank.‖ the cat answers. But he can‘t find the fish. When he sings and dances, the fish jumps back into the river.

as usual 像往常一样,像平常一样

suddenly adv. 突然地

forget v. 忘记

have a look at 看一看,看一眼

shout v. 叫,喊

bank n. 河岸

根据上文,选择正确的答案。

1. The cat goes to the river every day to ______.

A: catch fish

B: eat fish

C: play

2. One day, a fish comes out and he _________.

A: eats it

B: catches it

C: lets it go

3. The cat‘s friends come to see the fish, but they see _______.

A: nothing

B: a small fish

C: a big fish

4. Where is the fish at last (最后)?

A: In the basket.

B: In the river.

C: In the cat‘s mouth.

译文:

猫咪钓鱼

一只猫每天去河边,他想去钓鱼,但是他去钓不到一条。

一天,他像往常一样去了河边。突然一条鱼浮出了水面。他捉到了那条鱼。他非常开心。他忘记把鱼放到篮子里去了。他又唱又跳,叫道:―我捉到一条鱼!我捉到一条鱼!‖他所有的朋友都过来看。 ―你的鱼在哪儿?让我们看一看。‖他的朋友们说。

―在那儿,河岸附近。‖猫回答道。但是他找不到那条鱼。当他又唱又跳的时候,鱼跳回了河里。 参考答案:

1. A 2. B 3. A 4. B

Don‘t Throw Good Things Away

A man is going to the house of a rich man. He sees a box of good apples by the road. He says, ―I don‘t want them, because the rich man will give me a lot of good food.‖ Then he takes the apples and throws them into the dustbin. He comes to a river. The water in the river is very deep and he can‘t get across it. He says to himself, ―I can‘t go to the rich man‘s house today. ‖ So he goes home.

He has nothing to eat the day. He is very hungry, so he comes to the apples.

Don‘t throw good things away, you may be glad to have them sometimes.

dustbin n. 垃圾箱

himself n. 他自己

hungry adj. 饥饿的

across v. 穿过,从一边到另一边

根据短文回答下面的问题。

1. Where does the man find a box of apples?

2. Why he throws the apples away?

3. He can‘t go to the rich man‘s house, why?

4. Why the man is hungry and comes to the apples?

译文:

不要把好东西扔掉

有一个人要到一个富人家里去。在途中,他看到一箱很好的苹果。他说:―我不需要它们,因为富人会给我许多好吃的。‖于是他拿起苹果将它们扔进了垃圾箱。

他来到一条河边。河里的水很深他过不去。他自言自语说:―我今天去不成富人的家了。‖于是他回家了。

{写英语故事}.

这一天他什么都没吃,他很饿,所以他又找苹果去了。

不要扔掉好的东西,你可能偶尔会用到它们。

参考答案:

1. On his way to the rich man‘s house.

2. He thinks he can eat good things soon.

3. Because he can‘t go across the river.

4. Because he has nothing to eat that day.{写英语故事}.

It‘s My Bag

It‘s Sunday. There are many people in the bus. And an old man is looking here and there. He wants to find an empty seat. Then he finds one. He goes to it. A small bag is on the seat. And a young man is beside it.

―Is this seat empty?‖ asks the old man.

―No, it‘s for an old woman. She went to buy some bananas,‖ says the man. ―Well, let me sit here, please, I‘ll leave here when she comes back.‖

The bus starts. ―She hasn‘t come, but her bag is here. Let me give her the bag. ‖ Then the old man throws the bag out.

The young man shouts, ―Don‘t throw it! It‘s may bag!‖

empty adj. 空的

beside prep. 在…旁边

leave v. 离开

throw v. 扔

根据上文,判断下面各题的对与错,正确的写―F‖,错误的写―T‖。

1. The bag on the empty seat is the young man‘s.

2. The empty seat is besides to old man.

3. The young man throws the bag out.

4. The old woman shouts to the old man.

译文:

这是我的包

今天是周末,公共汽车上有许多人。一位老人站在车上到处看,他想要找到一个空的座位。后来他发现了一个,他走了过去。有一个小包在座位上,有一个年轻的男子坐在这个座位的旁边。

―这个座位有人吗?‖老人问道。

―有,这是一位老太太的座位。她买香蕉去了。‖男子说道。―那么请先让我坐一下吧,等她回来我就会离开。‖ 公车开动了,―她还没回来,可是她的包还在这里,我把这包还给她吧。‖说着老人就把包扔到车外。 年轻男子喊道:―不要扔!那是我的包!‖

参考答案:

1. T 2. F 3. F 4. F

The Monkey

A monkey is hungry. He wants to look for something to eat. At this time, he sees many peaches on the trees. So he climbs the trees and picks up the peaches.

Suddenly he sees many bananas on other trees. He then jumps down and runs to the banana trees. Every banana is big and yellow. He is very happy. Then he sees many watermelons on the ground. He begins to pick up the watermelons.

A hare comes up. The monkey sees the hare. Then he runs after it.

In the end, the monkey gets nothing.

peach n. 桃子

climb v. 爬

pick up 摘{写英语故事}.

watermelon n. 西瓜

ground n. 地上

begin v. 开始

hare n. 野兔

根据上文,判断下面各题的对与错,正确的写―F‖,错误的写―T‖。

1. The monkey sees many peaches on the ground.

2. The monkey doesn‘t run after the hare.

3. The bananas are big and yellow.

4. The monkey doesn‘t get anything.

译文:

猴子

一只猴子饿了。他想找些吃的。这时,他看到树上有很多桃子。所以他爬去摘桃子。

突然,他看到其它树上有许多香蕉。然后他就跳下来,向香蕉树跑去。每个香蕉又大又黄,他非常高兴。然后他看到地上长着许多西瓜,他又开始摘起西瓜来。

一只野兔出现了。猴子看到了兔子,就追上去。

最后,猴子什么也没有得到。

参考答案:

1. F 2. F 3. T 4. T

It Is Still Too Much

An old lady is very deaf. She thinks everything is too dear in the shop. One day, she wants to buy a hat. She goes into a shop and points to hat and asks.

―How much is it?‖

―Seven dollars, Madam,‖ the salesgirl answers, ―It is very cheap.‖

The old lady says, ―Seventeen dollars? It is too much. If it is fourteen dollars, I will buy it.

―Not seventeen dollars, Madam,‖ the girl says, ―but seven.‖

―It is still too much,‖ replies the old lady, ―If it is five dollars, I will buy it.‖

still adv. 还,仍

deaf adj. 聋的

point v. 指

salesgirl n. 女售货员

根据上文,判断下面各题的对与错,正确的写―F‖,错误的写―T‖。

1. The old lady is very deaf.

2. She thinks the hat is cheap.

3. The lady will buy the hat for fourteen dollars.

4. The hat sells seven dollars.

译文:

还是太贵

一位老太太耳聋了,她认为商店里的东西都太贵了。一天,她想买帽子。她走进一家商店,指着一顶帽子问道:{写英语故事}.

―这个多少钱?‖

―七美元,夫人,‖女店员说道:―这是很便宜的。‖

老太太说:―十七美元?太贵了。如果是十四美元,我就买啦。‖

―不是十七美元,夫人,‖女孩说道:―是七美元。‖

―还是太贵了,‖老太太回答道,―如果是五美元,我就买啦。‖

参考答案:

1. T 2. F 3. F 4. T

篇二:《英语小故事》

“Once upon a time, there was a king who had a daughter as beautiful as a blooming rose. To all the suitors who came to the king's palace to ask for the hand of the princess, the old king assigned three tasks to be accomplished, each next to impossible. One day, into the king's palace came a handsome young prince…" Well, you know the rest. The three tasks may be different in different versions, but the main plot is always the same, with the prince claiming the princess's hand triumphantly.

And the ending is always the same, finishing with the line "And they live happily every after." Why aren't we tired of something so fanciful, so unrealistic, and, I would say, so unimaginative? How can a story like that endure generations of repetition`? Because, I think, it is a typical success story. It is highly philosophical and symbolic. By implication, we see a 4-step definition of success: 1 ) a goal to be set. as represented by the beautiful princess; 2 ) challenges to be met, as represented by the three tasks; 3 ) the process of surmounting difficulties, as represented by the ordeals the youth goes through; and 4 ) the reward of success, as represented by the happy marriage.

The story not only caters to everyone's inward yearning for success, but also emphasizes the inseparability of the process and the result. The reward of success will be much amplified if the path leading towards it is treacherous, and vice versa. If a person inherits his father's millions and leads an easy life, he is not a successful person even in material terms, because there are no difficulties involved in his achieving affluence. The term "success", to be sure. will not sit still for easy definition. But as I understand it, the true meaning of success entails a combination of both the process and the satisfactory result of an endeavor. To clarify my view, let me give another analogy.

If we changed the rules of football, greatly enlarged the goal and sent away David Seaman or any other goal keeper, so that another David, namely David Beckham, could score easily, then scoring would not give him the thrill of accomplishment and the joy that it brings. If we further changed the rules by not allowing Arsenal's defenders to defend, so that Beckham needed only to lift a finger, actually a toe, to score, then there would be no game at all, because the meaning of winning would have disappeared. In accepting the challenge, in surmounting the difficulties and in enduring the hardship, success acquires its value. The sense of attainment varies in proportion to the degree of difficulties on overcomes.

The concept of success is not constant but relative because the nature of difficulty is also relative. Something you do effortlessly might pose a great difficulty for a handicapped person. In acquiring the ability to do the same as you can, he or she achieve success. That's why we greatly admire Stephen Hawking, because, though confined to a wheel chair, he has contributed greatly to the field of science.

I myself, a rather shy person by nature who easily suffer from stage fright, had to pluck up great courage to take part in a speech contest like this. I could have stayed away and had an easy time of it by not entering the university level contest.But I chose to accept the challenge and to face the difficulties. Now here I am. If I come out first, it will be a great success for me. If I come out last-I hope this will not be the case-but if I come out last, I will not call my attempt a failure, but will also celebrate it as a true success, because part of my goal is my own character training-to do more assertive, to be brave in face of difficulties. For me, it is a meaningful step forward, small as it is, in the long journey toward the final success in my life, because I have truly gained by participating.

Let us return to our handsome young prince and the 4-step definition of success. You my have noticed that the usual worldly criteria of wealth, position and fame were not mentioned as part of the story, but rather, it emphasized the process of overcoming difficulties. The ancient wisdom had already defined the meaning of success, and this is my definition, too.

Thank you.

译文:成功之我见

“很久以前,有个国王,他的女儿貌美如花。老国王向所有来求婚的男士提出了三个任务作为挑战,而每一项任务都异常艰巨,几乎不可能完成。一天,来了一位年轻英俊的王子……”好了,下面的故事你们都知道了。三项任务在不同的版本中各不相同,但关键部分的情节都如出一辙:王子成功地过关,得到了公主的芳心。而故事的结局也都一样,最后一句都写道:“从此他们幸福地生活在一起。

为什么我们对如此美妙、如此不切实际,而我要说,如此缺乏想象力的东西这么乐此不疲呢?这样的故事又如何能够经历几代人的重复?我想,因为它是典型的成功的例子。故事的思想性很强,具有代表性。通过故事带给我们的启示,我们认识到了成功定义中的四个步骤;第一,目标的设定,有如故事里美丽的公主;第二,所遇到的困难和挑战,就像三大任务;第三,克服困难的过程,故事中青年经历重重难关可以作为象征;第四,就是成功的果实,如同幸福的婚姻。

这个故事不仅迎合了人们内心深处对成功的向往,也强调了过程和结果的不可分离。如果通往成功的道路崎岖曲折,那么成功的回报必然硕果累累,反之亦然。如果一个人继承了父辈的百万家产而生活得轻松富足,那么,即使在物质上,他也不能算是个成功人士,因为,他的财富并没有经过艰难困苦而获得。确切地说,“成功”这个词,不是个静态简单的定义。在我的理解中,真正意义上的成功是奋斗的过程和经历了奋斗之后赢得的满意的结果。请让我另举一例来阐明我的见解。

如果我们试着改变足球的比赛规则,将球门放得很大,换下大卫?希曼或其他任何的守门员,这样,随便哪个“大卫”,比如说,“大卫?贝克汉姆”,就可以轻松进球,然而这样进一球却不能给他带来成功的震颤与喜悦。如果我们再改一改比赛规则,不让阿森纳队的防守来守门,那么,贝克汉姆只要动动手,其实就是抬抬脚就能进一球,那样的话、,实际上也没有什么比赛可言了,因为赢球的意义已经不存在了。在接受挑战、克服困难和经历磨难的过程中,“成功”的价值才得以丰满。取得成果的意义和所克服的艰难的程度成正比。所谓成功的概念不是一成不变的.而昙相对而言的,因为困难的性质也是相对意义上的。

正常人不费力气做成的事对于一个残疾人来说也许相当困难。获得了同正常人一样的能力,这个残疾人就获得了成功。这便是我们为什么崇敬史蒂芬?霍金的原因—虽然行动不便,受到了轮椅的限制,他依然为科学界作出了巨大的贡献。

就我自己而言,生性羞涩,容易怯场,不得不鼓起非常大的勇气来参加此次的演讲比赛。我完全可以待在一边,不参加大学级别的比赛,而落得轻松自在。可是,我还是选择了接受这一挑战来面对困难。现在我来了,如果我能够得第一的话.这对我来说就是巨大的成功。如果,我是最后一名—我希望情况不是这样—但如果我真的是最后一名,我也不会认为这次的尝试是一次失败,反而我要把它当作一次真正的成功来庆贺,因为我一部分的目标是对自己性格的锻炼—更加坚强、勇敢地面对困难。对我来说,这标志着我在通向成功人生的漫漫征途中又向前迈进了一步,尽管是很小的一步,但是我确实通过参与真正地获得了收益。 回到我们年轻英俊的王子和对“成功”的四步骤定义上吧,您也许已经注意到了财富、地位和名誉等这些世俗的标准在故事中并未提及,相反故事强调了克服重重困难的过程。古代的智慧已经对成功的意义下了定义,这也是我的定义。

篇三:《英语小故事》

英语小故事

Breakfast or lunch?

It was Sunday. I never get up early on Sundays. I sometimes stay in bed until lunchtime. Last Sunday I got up very late. I looked out of the window. It was dark outside. 'What a day!' I thought. 'It's raining again.' Just then, the

telephone rang. It was my aunt Lucy. 'I've just arrived by train,' she said. 'I'm coming to see you.'

'But I'm still having breakfast,' I said.{写英语故事}.

'What are you doing?' she asked.

'I'm having breakfast,' I repeated.

'Dear me,' she said. 'Do you always get up so late? It's one o'clock!'

问题:

1.Does the writer always get up early on Sundays,ordoes he always get up late?

2.Did he geu up early last Sunday,or did he get up late?

3.Who telephone then?

4.Had she just arrived by train,or had she come on foot?

5.Was she coming to see him or not?

6.Did he say,’I’m still having breakfast",or did he say,"I am still in bed'?

7.Was his aunt very urprised or not?

8.What was the time?

答案:

1 no , writer never got up early on sundays

2 no , he didn`t got up early on last sunday

3 writer`s aunt lucy.

4 she just arrived by train.

5 yes she was coming to see him

6 writer said"’I’m still having breakfast"

7 she was very surprised when she knows writer just got up.

8 it was 1`clock

Reward for Virtue

My friend, Hugh, 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 Hugh 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 Hugh 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!

问题和答案:

1Is Hugh fat or not? Yes.

2Has he gone on a diet or not? Yes.

3Has he forbidden himself all the foods he likes, or has he forbidden himself all the foods he does not like? He has forbidden himself all the foods he likes.

4Has he lost weight or not when the writer visited him? No.

5What did he hide whenthe writer visited himyesterday? A large parcel.

6Why did Hugh say that he had to reward himself occasionally? His diet was too strict.

7Did the parcel contain chocolate and sweets, or did it contain biscuits? It contained five large bars of chocolate and three bags of sweets!

Am I all right?

While John Gilbert was in hospital, he asked his doctor to tell him whether his operation had been successful, but the doctor refused to do so. The following day, the patient asked for a bedside telephone. When he was alone, he

telephoned the hospital exchange and asked for Doctor Millington. When the doctor answered the phone, Mr. Gilbert said he was inquiring about a certain patient, a Mr. John Gilbert. He asked if Mr. Gilbert's operation had been

successful and the doctor told him that it had been. He then asked when Mr. Gilbert would be allowed to go home and the doctor told him that he would have to stay in hosptial for another two weeks. Then Dr. Millington asked the caller if he was a relative of the patient. 'No,' the patient answered, 'I am Mr. John Gilbert.'

问题和答案:

1What did Dr.Millington refuse to tell his patient,John Gilbert?

He refused to tell his patient whether his operation had been successful.

2.Why did the doctor tell John Gilbert on the phone about his operation the following day?

Because the doctor thought the caller was a different person,he thought it could be a relative of John Gilbert.

3.According to the doctor, when would Mr.Gilbert be allowed to go home?

According to the doctor, when would Mr.Gilbert be allowed to go home?

E是等腰梯形一腰CB的中点,EF⊥AD,垂足为F,求证:S梯形ABCD=AD·EF 如图,连接AE交BC的延长线于G点,连接BE,

∵DE=EC,CG=DA,∠ADE=∠ECG,

∴△ADE≌△GCE(SAS),

∴:AE=GE,

∴可得:S△ABG=S梯形ABCD=2S△ABE=AB×FE.

如图所示在直角梯形ABCD中,AD//BC,∠B=90°,AD=24cm,AB=8cm,BC=26cm,动点P、Q分别从A、C同时出发,点P以1cm/s的速度由A向D运动,点Q以3cm/s的速度由C向B运动,当其中一点到达一端时,另一点也随之停止运动。求几秒钟后,四边形PQCD成为等腰梯形。

∵P,Q分别从A,C同时出发,动点P沿AD边以1CM秒的速度向D运动,动点Q沿CB边以3CM秒的速度向B运动

且AD=24CM,BC=26CM,AD‖BC,∠B=90度

∴在T秒内,动点P运动的距离是T厘米,动点Q运动的距离是3T厘米

即AP=T(厘米),DP=AD-AP=24-T(厘米),CQ=3T(厘米)

∵要使四边形PQCD是平行四边形,必有CQ=DP,即3T=24-T……..(1)

要使四边形PQCD是等腰梯形,必有CQ=DP+2(BC-AD),即3T=24-T+2*2……..(2)

∴解方程(1)得 T=6(秒)

解方程(2)得 T=7(秒)

故当运动时间为6秒时,四边形PQCD是平行四边形。当运动时间为7秒时,四边形PQCD是等腰梯形。 如图,平面上的四边形 ABCD 是一只"风筝"的骨架,其中 AB=AD,CB=CD. (1)九年级王云同学观察了这个 风筝"的骨架后, 九年级王云同学观察了这个" (1)九年级王云同学观察了这个"风筝"的骨架后,他认为四边形 ABCD 的两条对角线 AC⊥BD,垂足为 E, 你同意王云同学的判断吗?请充分说明理由; 并且 BE=ED,你同意王云同学的判断吗?请充分说明理由; 的面积. (2)设对角线 AC=a,BD=b,请用含 a,b 的式子表示四边形 ABCD 的面积.

根据题设,

(1)∵AB=AD,

∴点A在BD的垂直平分线上.

∵CB=CD,

∴点C在BD的垂直平分线上.

∴AC为BD的垂直平分线,BE=DE,AC⊥BD.

(2)由(1)得AC⊥BD.

∴SABCD=S△CBD+S△ABD=1/2BDoCE+1/2BDoAE=1/2BDoAC=1/2ab.

设BD的中点为F,连结AF、CF。由于AB=AD,所以AF⊥BD,同理CF⊥BD。根据过直线上一点有且只有一条直线与已知直线垂直可知,AFC共线,所以F即为E点。

由此,我们可以推断AC⊥BD,BE=ED。{写英语故事}.

(2)四边形ABCD可以拆分为△ABD与△BCD。

S(ABD)=1/2(DB×AE),S(BCD)=1/2(DB×EC)

所以S(ABCD)=1/2(DB×(AE+EC))=1/2(DB×AC)=1/2ab

如图,在等腰梯形ABCD中,已知AD∥BC,AB=DC,AD=2,BC=4,延长BC到E,使CE=AD.

(1)写出图中所有与△DCE全等的三角形,并选择其中一对说明全等的理由;

(2)探究当等腰梯形ABCD的高DF是多少时,对角线AC与BD互相垂直?请回答并说明理由.

解:(1)△CDA≌△DCE,△BAD≌△DCE;(2分)

①△CDA≌△DCE的理由是:

∵AD∥BC,

∴∠CDA=∠DCE.(3分)

又∵DA=CE,CD=DC,(4分)

∴△CDA≌△DCE.(5分)

②△BAD≌△DCE的理由是:

∵AD∥BC,

∴∠CDA=∠DCE.(3分)

又∵四边形ABCD是等腰梯形,

∴∠BAD=∠CDA,

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