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凹凸个性教育初二升初三第八课

凹凸个性教育初二升初三数学第八课

学习内容：正方形

本节知识点：

一、正方形的定义：有并且有．的平行四边形

．．．．．叫做正方形．

二、正方形有什么性质:

边：______________________________________________________

角：________________________________________________________

对角线：___________________________________________________

例题：1、如图，E为正方形ABCD内一点，且△EBC是等边三角形，

求∠EAD与∠ECD的度数．

2、已知：如图，正方形ABCD中，对角线的交点为O，E是OB上的一点，DG⊥AE 于G，DG交OA于F．求证：OE=OF．

三、正方形的判定

1、____________________________________________________________

2、___________________________________________________________

3、__________________________________________________________

4、___________________________________________________________

例题：1、下列说法是否正确，并说明理由．

①对角线相等的菱形是正方形；（）

②对角线互相垂直的矩形是正方形；（）

③对角线垂直且相等的四边形是正方形；（）

④四条边都相等的四边形是正方形；（）

⑤四个角相等的四边形是正方形．（）

E F O D C

B A 例题：已知：如图，△AB

C 中，∠C=90°，C

D 平分∠ACB ，D

E ⊥BC 于E ，D

F ⊥AC 于F ．求证：四边形CFDE 是正方形．

课堂检测

1、如图，在正方形ABCD 中，点G 是BC 上任意一点，连接AG ，过B ，D 两点分别作BE ⊥AG ，DF ⊥AG ，垂足分别为E ，F 两点，求证：△ADF ≌△BAE .

2、如图，正方形ABCD 的对角线AC 、BD 交于点O ，∠OCF ＝∠OBE ．求证：OE ＝OF

3、已知：如图，在△ABC 中，AB=AC ，AD ⊥BC ，垂足为点D ，AN 是△ABC 外角∠CAM 的平分线，CE ⊥AN ，垂足为点E.

（1）求证：四边形ADCE 为矩形；

（2）当△ABC 满足什么条件时，四边形ADCE 是一个正方形？并给出证明．

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初二升初三试题一 . 单项选择。（ 20 分） ( )1. It’ s not polite to speak in public. A. loud B. loudly C. louder ( )2.Your bike is my sister’ s. A. same as B. as the same C. the same as ( )3. I’ m in any book. A. interested; interesting B. interesting; interested C. interests; interest ( )4. ________ youngest leader in our school is________ man called Janson . A. The； a B. A ；the C. A； a D. An ；an ( )5. He asked his father. A. where it happens B. what was happen C. how it happened ( )6. I don’ t know he will come tomorrow,he come, I will tell you. A. if; whether B. whether; whether C. whether; if ( )7. ——will you stay in America? —— About two months. A. How many B. How often C. How long ( )8. He found very interesting to ride a horse on the farm. A. this B. that C. it ( )9. His parents make her at night. A. stay at home B. stags at home C. to stay at home ( )10. Which do you like, Jeans or cheongsam? A. good B. better C. well ( )11. Tom realized that he ________ his physics book at home when he reached school. A. left B. had left C. was leaving D. leaves ( )12 _______ Sarah _______ Lina is going to play basketball because they both like it very much. A . Both ,and B. Neither, nor C. Not only , but also D. Either, or ( )13. —— Did Jack come to our party yesterday? —— No, he. A. wasn ’ t invited B. isn’ t invited C. didn’ t invite ( )14. You worry about him. He will get well soon. A. needn ’t B. can ’t C. mustn ’t () 15. _______ difficult questions they are! I can’ t answer them. A. How B. How an C. What D. What an ()16---Would you mind booking two tickets for the film“ 2012”? ---_____, I’ m so busy now. I’ ll do it later. A Not at all B Sorry C Thank you D Of course ( )17. Oh, Danny. It’ s raining outside. You’ d betteryour raincoat. A. put on B. wear C. in D. dress