各位朋友，大家好！今天，我給大家分享一道初中數學中求陰影部分面積的題目，要解決這道題，必須添加輔助線作為三角形的高，再結合勾股定理和全等三角形才能解決問題。下面，我們就一起來看這道例題吧！
例題：（初中數學題）如圖，在正方形ABCD中，已知AB的長是2厘米，將線段BD繞點B順時針旋轉90°得到線段BF，將線段CD繞點C順時針旋轉90°得到線段CE，連接EF。求圖中陰影部分的面積是多少平方厘米？（結果保留π）
【課前預習】
【答案與解析】
在美國為首的北約計劃下，澤連斯基秘密下令制造“臟彈”。
A.On Tuesday
∵AE、AD、BD都是定值，
although some details have not been settled.
在△DCP和△BCE中，CD=BC, ∠DCP＝∠BCE，CP=CE，
n.①模式，式樣;②圖案，圖樣;v.仿制，模仿
author['?:θ?]n.作者 作家 創造者vt.創造 寫作
∴點A和點D都在線段BC的垂直平分線上（和一條線段兩個端點距離相等的點，在這條線段的垂直平分線上）
【總結升華】綜此題同樣是綜合運用了線段垂直平分線的定理及逆定理，同時注意，在三角形中，當給出一個角是90°時，另外兩角的和也是90°，是在直角三角形中推導角時經常用到的方法．
∵點E在AD上，
【例 1】 The townsfolk don’t see it this way and local (①) council does not
可當了皇帝后，他施政的觀點全是儒家的。所以矛盾的很，王莽這人應該是雙子座的，有雙重人格。
geometry[d?i'?mitri]n.幾何 幾何學
expansion[iks'p?n??n]n.擴大 擴充 擴張 膨脹
devices of different kinds that were usable in scientific experiments.
B. Because he wanted to find an excuse to kill Effendi.
【譯】 這種股東不了解他們所持股的公司里工人們的生活、思想和需求。他們對勞資
不在于它能多有效地壓制各種情感的表達， 而在于是否給予了人們思考和表達的最廣泛的自由，盡管有時這種結果會引起爭論和憤怒。”
其他
antenna[?n'ten?] n.(無線電或電視的)天線
friction['frik??n]n.摩擦 摩擦力 分歧
末節的汪洋大海之中”。
【譯】 皇家莎士比亞公司(RSC)聲稱是看戲的人給小鎮帶來了大部分收入，因為他們
冀教版九年級上冊英語各單元知識點歸納！第一單元知識點歸納
1.break a world record 打破世界記錄
2.get a gold medal 獲得金牌
3.with a time of … 用…時間
4.at the same time 同時
5.up and down 上上下下
6.set a world record創造世界記錄
7.as fast as possible 盡快
8.believe in sb 信任某人
9. make sb proud使某人感到自豪
10. give up 放棄
11.be able to do sth能夠做某事
12. at the age of …在…歲的時候
13.catch up with 趕上
14. none of 一個也沒有
15.fall off 掉下
16.do one’s best 盡某人的努力
17.the others 別的
第二單元知識點歸納
1. take turns 輪流, 交替
2. hold a world record 保持世界記錄
3. be located in / on ……位于
4. be proud of 以?自豪
5. on average 通常
6. on record 記載下來有
7. four times as --- as --- 是?四倍
8. think of 想出
9. find out 了解, 找出
10.some more 更多一些
11.try to do sth 試著去做某事
12.all over the world 遍及全世界
13.be full of 裝滿
14.it’s + adj.+ for sb to do sth
15.it’s time for sb to do sth
16.such as 例如
17.take part in 參與
18.that’s very kind of sb to do sth
第三單元知識點歸納
1.pay …for…付錢, 賠償
2.make money 掙錢
3.something to eat 吃的東西
4. what’s the price of …價錢是…
5. get up 起床
6.be hard to do sth 做某事難
7.come up to 到達
8.go over to 走過
9.give sth back to sb 把? 還給某人
10.do / deal with 處理
11.elementary school 小學
12.hold up 掛起
13.on the Internet 在互聯網上
14.what else別的什么
15.hear of 聽說
16.set up 創建
17.have success in 在…取得成功
18.anyother 別的
第四單元知識點歸納
1. wake up 醒來
2. what’s wrong with ……怎么了
3. get a cold 感冒
4. get dressed穿衣
5. be weak in 在? 薄弱
6. point to 指向?
7. look up 查字典
8. out of breath 上氣不接下氣
9. miss school 沒去上學
10. take medicine吃藥
11. breathe through the nose
12. must be 一定 表示推測否定:can’be
13. stay healthy 保持健康
14. be different from 不同于?
15. be made from /of由……制成
16. be bad for對..有害
17. get a pain in ?在?哪痛
18. dare to do sth 敢于做某事
19. think about 考慮
21. fall ill 生病
22. as soon as 一……就
23. the more, the better 越多越好
第五單元知識點歸納
1. be famous for 以…而著名
2. learn sth from 從…學到東西
3. be born in+地點 / on +時間:出生于…
4. not …until …直到…才…
5. make a mistake 犯錯
6. so… that …如此…以至
7. so that 為了,以便
8. come up with 想出, 提出
9. in the 1960s 在二十世紀 六十年代
10. devote to do sth 致力于..
11. because of 因為
12. in one’s spare time 在空余時間
13. it’s said that 據說
14. nothing but 除了…什么也沒有
15. day after day 一天又一天
16. in a difficult situation 在困難情況下
17. talk about 談論
18. in the same year在同一年
19. give first aid 進行急救
21. in the Anti-Japanese War 在抗日戰爭中
22. die of 死于?
第六單元知識點歸納
1.have an accident 發生事故
2.take care of 照顧
3.warn sb ( not ) to do sth 提醒某人(不)干某事
4. there ‘s something wrong with …有毛病
5.stop sb from doing sth 阻止某人干某事 6.instead of 代替
7.long long ago 很久以前
8.be careful 小心
9.it takes sb sometime/some money to do sth花某…時間/金錢干某事
10.from then on 從那時起
11.don’t have to do sth 沒必要做某事
13. on the edge of 在?邊沿
14.hurt oneself 傷到自己
冀教版九年級下冊英語各單元知識點歸納！第一單元知識點歸納
1. know / learn …by heart 記住…背誦…
2. need todo sth 必須做某事
3. look / sound / feel / like …
4. think of 想起………
5. hear / see sb do / doing ……
6. start / end with…從…開始/以...結束
7. express oneself 表達自己
8. at the moment 此時
9. a set number of 一定數量的
10. either …or …或者…或者…
11. both ?and 兩者都.
12. fill in 填入
13.look up 向上看. 查字典
14.another two 另外兩個
15.differentkinds of 各種不同類型的
16.go ahead .向前 走吧 說吧 干吧
17.in the middle of 在?中間
18.be related to 與?有關
第二單元知識點歸納
1. combine …and ...和…結合 2. neither …or …既不…也不
3. the answer to the question:問題的答案
4. not only …but also…不僅…而且
5. the same as…與…一樣
6. divide sth in half 把某物分成兩半
7. no longer不再
8. had better ( not ) do sth 最好(別)干某事
9. play chess 下棋
10.say hello to sb 向某人問好
11.what if 如果……將會怎樣
12.generally speaking 通常來說
13.except for 除……外
14.for example例如
15.prefer……to 與……比較更喜歡?
16.prefer to do sth rather than do sth
第三單元知識點歸納
1. be different from 不同于……
2. make a mistake 犯錯
3. pick up 拾起 4. be full of 裝滿
5. keep doing sth 保持干某事 6. point to 指向?
7. introduce ? to ?把?介紹給?
8. eat up 吃光
9. as soon as 一…就…
10.talk about /with / to 交談
11.give sth back to sb 把某物還給?
12.have trouble with 在…遇到麻煩
13.face to face 面對面
14.at the end of在…的最后
15.in good Chinese tradition
16.no problem 沒問題
17.never mind 別擔心
18.depend on 依靠 視情況而定
19.again and again 反復地
21.give sth back to sb 把?還給
22.given name 名字 23.family name 姓氏
第四單元知識點歸納
1. spend sometime/some money on sth:在某事上花費?時間/金錢
2. have a fight with sb和某人爭吵
3. be bad for對?不利
4. have / hold a meeting 開會
5. be angry with sb/sth
6.agree to do sth 同意做某事
7. either of 兩個都
8. belong to 屬于
9. the student council 學生會
10.make a friend with sb 和某人交朋友
11.understand each other 相互了解
12.a number of 成員
13.the Garden of Eden 伊甸園
14.at last 最后
15.have a talk 談話
16.and so on 等等
17.to be honest 說實話
18.the Garden of Eden 伊甸園
第五單元知識點歸納
1. how do you feel about ……
2. teach sb sth 教某人某事
3. knock on /at the door敲門
4. hang up 把?掛起
5. it’ time for …到…時候了
6. help yourself to sth 請隨便吃……
7. turn on /off 打開/關閉
8. hand in /out 上交/分發
9. would you mind doing sth
10. it’s very kind of sb to do sth
11.be /get ready for 準備做?
12.get sth ready 準備好某物
13.be different from 不同于?
14.not ……at all一點也不
15.regard sth/sb as把某人/當作……
16.from now on 從現在起
17.three percent of 百分之三
18.compare to /with 與?相比
第六單元知識點歸納
1. grow up 長大
2. be free 有空,自由
3. be busy doing 忙于做某事
4. at first 首先
5. graduate from畢業于
6. up to 達到
7. pay attention to 注意
8. cut down 砍下
9. encourage sb to do sth 鼓勵某人做某事
10.make progress 取得進步
11.step by step 一步一步地
12.be worth doing sth 值得做某事
13.even if 即使. 縱然
14.get a chance to do sth 有機會干某事
15.as many as 230 million多達二億三千萬
16.leave for 起程去………
17.shout at 對……大聲喊
18.leave sb alone 讓某人單獨留下
19.spend one’s vacation 度過某人的假期
第I卷 非選擇題一、 單項選擇(共20小題，計20分)
1.There is b “h”and “u”in the word “huge”.
2.---Li Hua’s English is very good.
3.---What’s wrong with you,Cheng Li?
4.---What did LuXun do after he gave up medicine?
5.---Whydon’t you ask Tom to do it?
6.---Did you go toJane’s birthday party?
7.“Tom, afraid of speaking in public. You are no longer a small boy.”said Mum.
8.---People can not only use salt for meals.
9.---Is itpossible to be mad others?
10.They found useful advertise on thee Internet.
11.---Why was the plane put off?
12.---Dad,when will you be free? You agreed to go to the seaside with me four days ago.
13.---How long has this shop ?
14.---I have won the girls’ long jump.
15.---Can you him studying hard?
16.---What about some soy milk? They are full ofprotein?
17.--- is the price of the book?
18.---We’d better g out for a walk instead of TV.Don’t you think so?
19.We don’t know . It is said that she would come tomorrow.
二、完形填空(10分)
21.A.passed B.passing C.pass D.passes
22.A.will you B.do you
23.A.spend B.cost C.take D.pay
24.A.And B.Then C.But D.Or
25.A.Anything B.Something
26.A.another B.otheres
27.A.paid B.pays C.was paid D.pay
28.A.such B.so C.very D.quite
29.A.return back B.go away
三、閱讀理解(30分)(A)Sports City Bar
31.When can we enjoy the “Buy one,get one free”at Sports City Bar?
32.Who have free lunch at the Sunday Family Buffet?
33.If you are thirteen,you （）.
34.The Sports CityBar is on the floor.
35.How much will your father pay if he and your10-year old brother go to have lunch at the Sunday Family Buffet?
36.This story tells us .
37.The prime Minister died because（） .
38.Why did the king ask Effendi to tell him the date of Effendi’s own death?
39.The king let Effendi go because（） .
The book was started by Hugh Beaver from Britain. In1951,he went shooting birds and talked with his friends about the fastest birdin Europe. Three years later,they were still talking about it.
② An American woman Lee Redmond has the longest finger nails(指甲).They grew as long as 600mm! She made the record in 1971.
41.We can see everything in the Guinness Book ofRecords except .
42.The Guinness Book of Records has been one of the best sellingbooks for .
43.Newport thought many people tried to break Gunnessrecords because . A. their names be kept in the world records.
44.Which of the following is right according to thepassage?
C. The Guinness Book of Records started in the year1954.
45.The writer of this passage wants to 。
五、根據首字母和句子意思補全單詞。(5分)
46.I should do my homework tonight i of watching TV.
47.He decided to go there,no one could s him.
48. Smoking is bad for our health,so we should makesome posters a smoking. 49.He doesn’t have much m ,he is very poor.
六、用所給單詞的適當形式填空。(5分)
51.In 1809,Santa had eight (reindeer).
52.Most animals run on four (foot).
53.--What’s your ? --1.88m.(high)
54.Her grandfather told her not (water)the flowers ifit (rain).
55.Our class could play soccer for a week without (stop).
七、動詞填空。(15分)
Since 1946,one of the most important inventions hasbeen the computer. It has been changing all our lives.
The first computer 56 (build) in 1946. It 57 (be) aslarge as a room and very difficult and slow 58 (use). But since the inventionof silicon chip(硅片),computers 59 (become) smaller,easier and faster to operate. Somecomputers are as small as TV sets. Some can even be made smaller than a book.And computers 60 (get) smaller and smaller all the time. Who knows thecomputers of tomorrow 61 (be) like?
七、書面表達。(15分)
提示:1.What does your school look like?
2.What fun do you have at school?
3.Why do you like your school?
一、1-5BAACD 6-10BDCBC 11-15BBBDC 16-20BDDCD
二、21-25BADCD 26-30DCBCC
三、31-35DACDB 36-40ADBAD 41-45DADBC
四、45.instead 47.stop 48.against 49.money 50.including
五、51.reindeer52.feet 53.height 54.to water 55.stopping 六、56.was built 57.was 58.to use59.have become 60.are getting 61.will be 62.are 63.be put 64.works 65.doing
七、略