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全等三角形的性质及其判定定理(一)

全等三角形的性质及其判定定理(一)

武汉铭都教育培训中心(沌口校区)授课活页表年级七升八授课形式小班讲次第讲授课教师授课科目数学授课时间月日点- 点学生姓名:教学内容:全等三角形的性质及其判定定理(一)本节重点:教学设计:全等三角形一、创设情境,引入新课1、问题:各组图形的形状与大小有什么特点?一般学生都能发现这两个图形是完全重合的。

归纳:能够完全重合的两个图形叫做全等形。

2.学生动手操作⑴在纸板上任意画一个三角形ABC,并剪下,然后说出三角形的三个角、三条边和每个角的对边、每个边的对角。

⑵问题:如何在另一张纸板再剪一个三角形DEF,使它与△ABC全等?3.板书课题:全等三角形定义:能够完全重合的两个三角形叫做全等三角形“全等”用“≌”表示,读着“全等于”如图中的两个三角形全等,记作:△ABC≌△DEF二、探究全等三角形中的对应元素1. 问题:你手中的两个三角形是全等的,但是如果任意摆放能重合吗?该怎样做它们才能重合呢?2.学生讨论、交流、归纳得出:⑴.两个全等三角形任意摆放时,并不一定能完全重合,只有当把相同的角重合到一起(或相同的边重合到一起)时它们才能完全重合。

这时我们把重合在一起的顶点、角、边分别称为对应顶点、对应角、对应边。

⑵.表示两个全等三角形时,通常把表示对应顶点字母写在对应的位置上,这样便于确定两个三角形的对ABC D EO应关系。

全等三角形的性质1.观察与思考:寻找甲图中两三角形的对应元素,它们的对应边 有什么关系?对应角呢? 全等三角形的性质: 全等三角形的对应边相等. 全等三角形的对应角相等. 2.用几何语言表示全等三角形的性质 如图:∵∆ABC ≌ ∆DEF∴AB =DE ,AC =DF ,BC =EF (全等三角形对应边相等) ∠A =∠D ,∠B =∠E ,∠C =∠F (全等三角形对应角相等) 探求全等三角形对应元素的找法 1.动画(几何画板)演示(1)图中的各对三角形是全等三角形,怎样改变其中一个三角形的位置,使它能与另一个三角形完全重合? 归纳:两个全等的三角形经过一定的转换可以重合.一般是平移、翻折、旋转的方法. (2)说出每个图中各对全等三角形的对应边、对应角归纳:从运动角度可以很轻松解决找对应元素的问题.可见图形转换的奇妙. 2. 动画(几何画板)演示图中的两个三角形通过怎样的变换才能重合?用式子表示全等关系.并说出其中的对应关系.3. 归纳:找对应元素的常用方法有两种:(1)从运动角度看a .翻折法:一个三角形沿某条直线翻折与另一个三角形重合,从而发现对应元素.b .旋转法:三角形绕某一点旋转一定角度能与另一三角形重合,从而发现对应元素.c .平移法:沿某一方向推移使两三角形重合来找对应元素. (2)根据位置元素来推理FBACD E ⑴⑶CBDA⑵ABCDE FA BC DEOa.有公共边的,公共边是对应边;b.有公共角的,公共角是对应角;c.有对顶角的,对顶角是对应角;d.两个全等三角形最大的边是对应边,最小的边也是对应边;e.两个全等三角形最大的角是对应角,最小的角也是对应角; 三、课堂练习练习1.△ABD ≌△ACE ,若∠B =25°, BD =6㎝,AD =4㎝, 你能得出△ACE 中哪些角的大小,哪些边的长度吗?为什么 ? 练习2.△ABC ≌△FED⑴写出图中相等的线段,相等的角;⑵图中线段除相等外,还有什么关系吗?请与同伴交 流并写出来. 四、课堂小结通过本节课学习,我们了解了全等的概念,发现了全等三角形的性质,探索了找两个全等三角形对应元素的方法,并且利用性质解决简单的问题。

sss 英语儿歌 歌单

sss 英语儿歌 歌单

sss 英语儿歌歌单1. "Twinkle, Twinkle, Little Star"2. "Baa, Baa, Black Sheep"3. "Mary Had a Little Lamb"4. "Hickory Dickory Dock"5. "Humpty Dumpty"6. "Itsy Bitsy Spider"7. "Old MacDonald Had a Farm"8. "Row, Row, Row Your Boat"9. "This Little Piggy"10. "If You're Happy and You Know It"11. "Five Little Monkeys Jumping on the Bed"12. "One, Two, Three, Four, Five"13. "Ten in the Bed"14. "I'm a Little Teapot"15. "The Wheels on the Bus"16. "Five Little Ducks"17. "ABC Song"18. "Colors Song"19. "Shape Song"20. "Head, Shoulders, Knees and Toes"这些儿歌旋律简单、歌词重复,非常适合儿童学唱。

通过唱儿歌,孩子们可以提高英语听力和口语能力,同时也能培养音乐欣赏能力和节奏感。

您可以根据孩子的喜好和年龄选择适合的儿歌,与他们一起欢唱,享受英语学习的乐趣!。

sss量表评分标准

sss量表评分标准

sss量表评分标准SSS量表评分标准是主要用于评估一个人的社交焦虑症状的常用工具。

SSS量表全称为社交情境评定量表(Social Situations Scale),是由David Hope、Richard G. Heimberg、和Cindy L. Dodge等人于1990年制定的一种被广泛使用的社交焦虑评估工具。

社交焦虑症是一种常见的心理障碍,患者会感到在社交场合中非常不适,并经常出现出汗、心跳加速等身体症状。

SSS量表评分标准通过对患者在社交场合的各种情境的反应进行评估,从而判断患者的社交焦虑程度,并为治疗提供科学依据。

SSS量表一共包含24个社交情境,如和陌生人交谈、发表演讲、在晚会上与他人交流等。

每个情境的评分范围为0至5分,分值越高表示社交焦虑程度越高。

以下是SSS量表评分标准的具体解释:0分:对这种情境完全不焦虑1分:对这种情境有轻微的焦虑,但不影响正常的社交行为。

2分:对这种情境有明显的焦虑,但还可以进行正常的社交行为。

3分:对这种情境有显著的焦虑,社交行为可能会受到一定程度的限制。

4分:对这种情境极度焦虑,很难进行正常的社交行为。

5分:对这种情境极度恐惧,几乎无法进行社交行为。

通过对患者的SSS量表评分,医生可以根据不同的情境制定个性化的治疗方案。

治疗常包括药物治疗和心理治疗。

药物治疗主要是使用抗抑郁药、抗焦虑药等药物。

心理治疗包括认知行为疗法、暴露疗法、社交技能培训等。

SSS量表评分标准的应用范围不仅限于社交焦虑症患者,也适用于其他情况下的社交焦虑评估。

SSS量表已经被广泛运用于临床研究和实践中,成为评估社交焦虑症状的重要工具之一。

最新人教版八年级上册数学第十二章全等三角形第11课时 三角形全等的判定(1)——SSS

最新人教版八年级上册数学第十二章全等三角形第11课时   三角形全等的判定(1)——SSS
求△AEC各内角的度数.
解:在△ABC与△AEC中,
= ,
ቐ = ,
= ,
∴△ABC≌△AEC(SSS).
∴∠B=∠E=30°,∠ACE=∠ACB=85°.
∴∠CAE=180°-∠E-∠ACE=65°.
返回目录
8. 如图11-12,点A,C,F,D在同一条直线上,AB=DE,BC=EF,
AC=DF,CE=FB,求证:△ABC≌△DEF.
证明:∵CE=BF,
∴CE+BE=BF+BE,
即CB=FE.
= ,
在△ABC和△DEF中,ቐ = ,
= ,
∴△ABC≌△DEF(SSS).
返回目录
7. 如图11-11,AB=AE,BC=EC,∠B=30°,∠ACB=85°,
【例2】如图11-4,点A,D,B,E在同一条直线上,AC=EF,
AD=EB,BC=DF.求证:(1)△ABC≌△EDF;(2)∠C=∠F.
证明:(1)∵AD=EB,∴AD+BD=EB+BD.
∴AB=ED.在△ABC与△EDF中,
= ,
ቐ = ,
= ,
∴△ABC≌△EDF(SSS).
返回目录
5.如图11-9,点C是AB的中点,AD=CE,CD=BE. 求证:
△ACD≌△CBE.
证明:∵点C是AB的中点,
∴AC=BC.
在△ACD和△CBE中,
= ,
ቐ = ,
= ,
∴△ACD≌△CBE(SSS).
返回目录
B组
6. 如图11-10,点C,E,B,F在同一条直线上,AB=DE,
∴∠DAE=∠BAC.
∵AB⊥AC,∴∠BAC=90°.

12.2.1三角形全等的判定(sss)(教案)

12.2.1三角形全等的判定(sss)(教案)
3.能够运用sss判定解决实际问题,如图形的拼接、角度和边长的确定等。
4.通过实际操作和例题解析,加深对三角形全等判定sss公理的理解和运用。
二、核心素养目标
《12.2.1三角形全等的判定(sss)(教案)》
本节课的核心素养目标旨在培养学生的以下能力:
1.空间观念与几何直观:通过sss全等判定的学习,使学生能够建立起三角形全等的直观认识,提高空间想象能力。
其次,在小组讨论和实验操作环节,学生们表现出了很高的积极性。他们通过合作交流,共同探讨三角形全等判定的应用,不仅加深了对知识点的理解,还提高了合作能力和解决问题的能力。但我也注意到,有些小组在讨论过程中,对于如何运用sss判定仍然存在一些疑问。这提示我在今后的教学中,需要更加关注学生的个体差异,给予他们针对性的指导。
举例:在复杂图形中,找到与题目相关的三角形,并从图中获取已知和求证的信息,进而运用sss判定解决问题。
(4)培养几何直观和空间观念,尤其在解决实际问题时,能够通过观察、分析图形,找到解题的关键信息。
举例:在实际问题中,通过观察和思考,发现隐藏在图形中的全等关系,从而找到解题思路。
四、教学流程
《12.2.1三角形全等的判定(sss)(教案)》
举例:在解决具体问题时,判断哪些信息是已知的,哪些需要求证,从而选择合适的全等判定方法。
(2)正确使用几何符号和术语,避免在证明过程中出现逻辑错误或符号错误。
举例:在证明过程中,要注意区分“=”、“≌”等符号,以及正确使用“对应边”、“对应角”等术语。
(3)在复杂图形中,识别并提取出全等三角形的相关信息,将实际问题转化为几何问题进行解决。
2.逻辑推理与证明能力:通过分析、归纳和推理,让学生掌握sss全等判定的逻辑基础,培养严谨的逻辑推理能力和几何证明技巧。

人教版数学七年级上册《三角形全等的判定(1)SSS》教案

人教版数学七年级上册《三角形全等的判定(1)SSS》教案

人教版数学七年级上册《三角形全等的判定(1)SSS》教案一. 教材分析《三角形全等的判定(1)SSS》是人教版数学七年级上册的一章,主要介绍了三角形全等的判定方法之一——SSS(Side-Side-Side)。

本节课通过讲解和实例分析,让学生理解并掌握SSS判定方法,能够运用SSS证明两个三角形全等。

二. 学情分析学生在学习本节课之前,已经掌握了三角形的基本概念和性质,能够识别和判断三角形的类型。

但是,对于三角形全等的判定方法,他们可能还比较陌生。

因此,在教学过程中,需要注重引导学生理解和掌握SSS判定方法。

三. 教学目标1.让学生理解三角形全等的概念,掌握SSS判定方法。

2.培养学生运用SSS判定方法解决实际问题的能力。

3.提高学生的空间想象能力和逻辑思维能力。

四. 教学重难点1.教学重点:SSS判定方法的理解和运用。

2.教学难点:对于复杂图形的SSS判定方法的运用。

五. 教学方法采用问题驱动法、案例教学法和小组合作学习法。

通过设置问题,引导学生自主探究和小组讨论,培养学生的解决问题能力和团队合作精神。

六. 教学准备1.准备相关的教学PPT和教学素材。

2.准备一些实际的三角形图形,用于讲解和练习。

七. 教学过程1.导入(5分钟)通过一个实际问题引出三角形全等的概念,例如:“在拼图游戏中,如何判断两个三角形是否完全一样?”让学生思考和讨论,引导学生认识到三角形全等的重要性。

2.呈现(10分钟)讲解三角形全等的定义和SSS判定方法。

通过PPT和实物图形,让学生直观地理解SSS判定方法。

举例说明SSS判定方法的应用,让学生初步掌握如何判断两个三角形全等。

3.操练(10分钟)让学生分组练习,每组提供一些实际的三角形图形,要求学生运用SSS判定方法判断两个三角形是否全等。

教师巡回指导,解答学生的疑问。

4.巩固(10分钟)通过一些综合性的题目,让学生运用SSS判定方法解决问题。

教师引导学生思考和讨论,帮助学生巩固所学知识。

人教版数学八年级上册12.2.1用SSS判定三角形全等教学设计

人教版数学八年级上册12.2.1用SSS判定三角形全等教学设计
1.帮助学生巩固全等三角形的定义,强化他们对全等概念的理解。
2.引导学生通过实际操作和探究,发现并理解SSS判定方法,提高他们的几何推理能力。
3.针对不同学生的学习特点,设计有针对性的教学活动,使他们在轻松愉快的氛围中掌握知识。
4.关注学生的学习情感,激发他们的学习兴趣,培养他们的自主学习能力。
在教学过程中,教师要关注学生的个体差异,充分调动他们的积极性,使他们在合作、交流、探索中不断提高,为后续几何知识的学习打下坚实基础。
-运用多媒体辅助教学,展示动态的几何图形,帮助学生形象地理解全等三角形的性质和判定方法。
-设计实际案例,让学生在解决问题的过程中,将理论知识与实际应用相结合。
2.教学步骤:
(1)导入新课:通过复习全等三角形的定义和已知判定方法,为新课的学习做好铺垫。
(2)自主探究:学生分组讨论,尝试运用SSS判定方法判断给定三角形是否全等,并总结规律。
4.鼓励学生运用所学知识,解决实际问题,培养他们的创新意识和应用能力。
(三)情感态度与价值观
在本节课的学习过程中,学生将形成以下情感态度与价值观:
1.培养学生对数学学习的兴趣,激发他们探索数学问题的热情。
2.培养学生的自信心,让他们在解决问题的过程中体验成功的喜悦。
3.培养学生严谨的学术态度,让他们明白在数学推理中,每一步都需要严谨的逻辑支撑。
人教版数学八年级上册12.2.1用SSS判定三角形全等教学设计
一、教学目标
(一)知识与技能
1.了解全等三角形的定义,知道全等三角形在形状和大小上完全相同。
2.熟练掌握用SSS(Side-Side-Side,即边-边-边)判定两个三角形全等的方法。
3.能够运用SSS判定方法,解决实际问题和几何证明题。

人教版数学八上第6讲全等三角形判定一(SSS,SAS)(基础)知识讲解(1)

人教版数学八上第6讲全等三角形判定一(SSS,SAS)(基础)知识讲解(1)

全等三角形判定一(SSS ,SAS )(基础)【学习目标】1.理解和掌握全等三角形判定方法1——“边边边”,和判定方法2——“边角边”; 2.能把证明一对角或线段相等的问题,转化为证明它们所在的两个三角形全等. 【要点梳理】要点一、全等三角形判定1——“边边边” 全等三角形判定1——“边边边”三边对应相等的两个三角形全等.(可以简写成“边边边”或“SSS ”).要点诠释:如图,如果''A B =AB ,''A C =AC ,''B C =BC ,则△ABC ≌△'''A B C .要点二、全等三角形判定2——“边角边” 1. 全等三角形判定2——“边角边”两边和它们的夹角对应相等的两个三角形全等(可以简写成“边角边”或“SAS ”).要点诠释:如图,如果AB = ''A B ,∠A =∠'A ,AC = ''A C ,则△ABC ≌△'''A B C . 注意:这里的角,指的是两组对应边的夹角.2. 有两边和其中一边的对角对应相等,两个三角形不一定全等.如图,△ABC 与△ABD 中,AB =AB ,AC =AD ,∠B =∠B ,但△ABC 与△ABD 不完全重合,故不全等,也就是有两边和其中一边的对角对应相等,两个三角形不一定全等.【典型例题】类型一、全等三角形的判定1——“边边边”1、已知:如图,△RPQ 中,RP =RQ ,M 为PQ 的中点.求证:RM 平分∠PRQ .【思路点拨】由中点的定义得PM =QM ,RM 为公共边,则可由SSS 定理证明全等. 【答案与解析】证明:∵M 为PQ 的中点(已知), ∴PM =QM在△RPM 和△RQM 中,()(),,RP RQ PM QM RM RM ⎧=⎪=⎨⎪=⎩已知公共边∴△RPM ≌△RQM (SSS ).∴ ∠PRM =∠QRM (全等三角形对应角相等). 即RM 平分∠PRQ.【总结升华】在寻找三角形全等的条件时有的可以从图中直接找到,如:公共边、公共角、对顶角等条件隐含在题目或图形之中. 把证明一对角或线段相等的问题,转化为证明它们所在的两个三角形全等,综合应用全等三角形的性质和判定. 举一反三:【变式】已知:如图,AD =BC ,AC =BD.试证明:∠CAD =∠DBC.【答案】证明:连接DC ,在△ACD 与△BDC 中()AD BC AC BDCD DC ⎧=⎪=⎨⎪=⎩公共边∴△ACD≌△BDC(SSS )∴∠CAD =∠DBC (全等三角形对应角相等) 类型二、全等三角形的判定2——“边角边”2、已知:如图,AB =AD ,AC =AE ,∠1=∠2.求证:BC =DE .【思路点拨】由条件AB =AD ,AC =AE ,需要找夹角∠BAC 与∠DAE ,夹角可由等量代换证得相等.【答案与解析】证明: ∵∠1=∠2∴∠1+∠CAD =∠2+∠CAD ,即∠BAC =∠DAE 在△ABC 和△ADE 中AB AD BAC DAE AC AE =⎧⎪∠=∠⎨⎪=⎩∴△ABC ≌△ADE (SAS )∴BC =DE (全等三角形对应边相等)【总结升华】证明角等的方法之一:利用等式的性质,等量加等量,还是等量.3、如图,将两个一大、一小的等腰直角三角尺拼接 (A 、B 、D 三点共线,AB =CB ,EB =DB ,∠ABC =∠EBD =90°),连接AE 、CD ,试确定AE 与CD 的位置与数量关系,并证明你的结论.【答案】AE =CD ,并且AE ⊥CD 证明:延长AE 交CD 于F ,∵△ABC 和△DBE 是等腰直角三角形 ∴AB =BC ,BD =BE 在△ABE 和△CBD 中90AB BC ABE CBD BE BD =⎧⎪∠=∠=︒⎨⎪=⎩∴△ABE ≌△CBD (SAS ) ∴AE =CD ,∠1=∠2又∵∠1+∠3=90°,∠3=∠4(对顶角相等) ∴∠2+∠4=90°,即∠AFC =90° ∴AE ⊥CD【总结升华】通过观察,我们也可以把△CBD 看作是由△ABE 绕着B 点顺时针旋转90°得到的.尝试着从变换的角度看待全等.举一反三:【变式】已知:如图,AP 平分∠BAC ,且AB =AC ,点Q 在PA 上,求证:QC =QB【答案】证明:∵ AP 平分∠BAC ∴∠BAP =∠CAP 在△ABQ 与△ACQ 中∵∴△ABQ ≌△ACQ(SAS) ∴ QC =QB类型三、全等三角形判定的实际应用4、“三月三,放风筝”.下图是小明制作的风筝,他根据DE =DF ,EH =FH ,不用度量,就知道∠DEH =∠DFH .请你用所学的知识证明.【答案与解析】证明:在△DEH 和△DFH 中,DE DF EH FH DH DH ⎧⎪⎨⎪=⎩==∴△DEH ≌△DFH(SSS) ∴∠DEH =∠DFH .【总结升华】证明△DEH ≌△DFH ,就可以得到∠DEH =∠DFH ,我们要善于从实际问题中抽离出来数学模型,这道题用“SSS ”定理就能解决问题. 举一反三: 【变式】工人师傅经常利用角尺平分一个任意角,如图所示,∠AOB 是一个任意角,在边OA ,边OB 上分别取OD =OE ,移动角尺,使角尺两边相同的刻度分别与D 、E 重合,这时过角尺顶点P 的射线OP 就是∠AOB 的平分线,你能先说明△OPE 与△OPD 全等,再说明OP 平分∠AOB 吗?【答案】证明: 在△OPE 与△OPD 中∵OE OD OP OP PE PD =⎧⎪=⎨⎪=⎩∴ △OPE ≌△OPD (SSS )∴ ∠EOP =∠DOP(全等三角形对应角相等) ∴ OP 平分∠AOB.【巩固练习】 一、选择题1. △ABC 和△'''A B C 中,若AB =''A B ,BC =''B C ,AC =''A C .则( ) A.△ABC ≌△'''A C B B. △ABC ≌△'''A B C C. △ABC ≌△'''C A B D. △ABC ≌△'''C B A2. 如图,已知AB =CD ,AD =BC ,则下列结论中错误的是( ) A.AB ∥DC B.∠B =∠D C.∠A =∠C D.AB =BC3. 下列判断正确的是( ) A.两个等边三角形全等B.三个对应角相等的两个三角形全等C.腰长对应相等的两个等腰三角形全等D.直角三角形与锐角三角形不全等4. 如图,AB 、CD 、EF 相交于O ,且被O 点平分,DF =CE ,BF =AE ,则图中全等三角形的对数共有( )A. 1对B. 2对C. 3对D. 4对5. 如图,将两根钢条'AA ,'BB 的中点O 连在一起,使'AA ,'BB 可以绕着点O 自由转动,就做成了一个测量工件,则''A B 的长等于内槽宽AB ,那么判定△OAB ≌△''OA B 的理由是( )A.边角边B.角边角C.边边边D.角角边6. 如图,已知AB ⊥BD 于B ,ED ⊥BD 于D ,AB =CD ,BC =ED ,以下结论不正确的是( ) A.EC ⊥AC B.EC =AC C.ED +AB =DB D.DC =CB二、填空题7. 如图,AB =CD ,AC =DB ,∠ABD =25°,∠AOB =82°,则∠DCB =_________.8. 如图,在四边形ABCD 中,对角线AC 、BD 互相平分,则图中全等三角形共有_____对.9. 如图,在△ABC 和△EFD 中,AD =FC ,AB =FE ,当添加条件_______时,就可得△ABC ≌△EFD (SSS )10. 如图,AC =AD ,CB =DB ,∠2=30°,∠3=26°,则∠CBE =_______.11. 如图,点D在AB上,点E在AC上,CD与BE相交于点O,且AD=AE,AB=AC,若∠B =20°,则∠C=_______.12. 已知,如图,AB=CD,AC=BD,则△ABC≌,△ADC≌ .三、解答题13. 已知:如图,四边形ABCD中,对角线AC、BD相交于O,∠ADC=∠BCD,AD=BC,求证:CO=DO.14. 已知:如图,AB∥CD,AB=CD.求证:AD∥BC.分析:要证AD∥BC,只要证∠______=∠______,又需证______≌______.证明:∵ AB∥CD (),∴∠______=∠______ (),在△______和△______中,⎪⎩⎪⎨⎧===),______(______),______(______),______(______ ∴ Δ______≌Δ______ ( ). ∴ ∠______=∠______ ( ). ∴ ______∥______( ).15. 如图,已知AB =DC ,AC =DB ,BE =CE 求证:AE =DE.【答案与解析】 一.选择题1. 【答案】B ;【解析】注意对应顶点写在相应的位置. 2. 【答案】D ;【解析】连接AC 或BD 证全等. 3. 【答案】D ; 4. 【答案】C ;【解析】△DOF ≌△COE ,△BOF ≌△AOE ,△DOB ≌△COA. 5. 【答案】A ;【解析】将两根钢条'AA ,'BB 的中点O 连在一起,说明OA ='OA ,OB ='OB ,再由对顶角相等可证.6. 【答案】D ; 【解析】△ABC ≌△EDC ,∠ECD +∠ACB =∠CAB +∠ACB =90°,所以EC ⊥AC ,ED +AB =BC +CD =DB.二.填空题7. 【答案】66°;【解析】可由SSS 证明△ABC ≌△DCB ,∠OBC =∠OCB =82412︒=︒, 所以∠DCB = ∠ABC =25°+41°=66°8. 【答案】4;【解析】△AOD ≌△COB ,△AOB ≌△COD ,△ABD ≌△CDB ,△ABC ≌△CDA. 9. 【答案】BC =ED ; 10.【答案】56°;【解析】∠CBE =26°+30°=56°. 11.【答案】20°;【解析】△ABE ≌△ACD (SAS ) 12.【答案】△DCB ,△DAB ;【解析】注意对应顶点写在相应的位置上. 三.解答题13.【解析】证明:在△ADC 与△BCD 中,,,,DC CD ADC BCD AD BC =⎧⎪∠=∠⎨⎪=⎩()...ADC BCD SAS ACD BDC OC OD ∠=∠=∴△≌△∴∴ 14. 【解析】3,4; ABD ,CDB ; 已知;1,2;两直线平行,内错角相等; ABD ,CDB ; AB ,CD ,已知; ∠1=∠2,已证; BD =DB ,公共边; ABD ,CDB ,SAS ;3,4,全等三角形对应角相等; AD ,BC ,内错角相等,两直线平行.15.【解析】证明:在△ABC 和△DCB 中AB DC AC DB BC =CB ⎧⎪⎨⎪⎩==∴△ABC ≌△DCB (SSS ) ∴∠ABC =∠DCB , 在△ABE 和△DCE 中ABC DCB AB DC BE CE =⎧⎪∠=∠⎨⎪=⎩∴△ABE ≌△DCE (SAS ) ∴AE =DE.DBA。

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20120308They're called hydrogels: Jell-O like materials made of networks of long-chain molecules in water.And they're as flexible as living tissue.But hydrogels could not recover from a cut—until now. Bioengineers at UC San Diego have made hydrogels that are self-healing in acidic conditions.When you cut open a piece of hydrogel, the polymers that normally entwine to hold the gel together cannot grasp each other again,leaving the wound unhealed.But in the new gels, additional molecular chains dangle from the primary structure. When two pieces of the cut hydrogel are pressed together in an acidic solution,the side chains of each piece tangle up to weld the parts together.The work is in the Proceedings of the National Academy of Sciences.These hydrogels could seal up industrial acid leakages and contribute to self-healing plastics.In the acidic environment of the stomach, they could bandage holes or deliver drugs to ulcers.The researchers are trying to make gels that mend at a range of pH levels.They may look like desserts, but self-healing hydrogels could be a medical main course.—Sophie BushwickHydrogel:水凝胶Jell-O:果冻Cut open 剖,切开Polymer 聚合物Entwine 缠绕,盘绕Gel 凝胶,冻胶Dangle 摇晃地悬挂着dangle from 在(扣栓处、系牢处等)摇晃地悬挂,从…吊着: Tangle up 缠在一起Weld 焊接,使结合Proceeding n. 进行;程序;诉讼;事项v. 开始;继续做;行进(proceed的ing形式)Seal up 密封住Leakage 泄露,渗漏物Bandage 绷带,用绷带包扎Ulcer 溃疡Mend 修理,修补It sounds like the premise for a bad police drama, maybe NYPD Chimp. But scientists have found that high-ranking chimpanzees can act like cops:intervening to settle public disputes.The study appears in the journal Public Library of Science ONE.In any community, conflicts inevitably arise. That's why we humans have law enforcement agencies, the military and impartial arbitrators like Jerry Springer. But how does our closest kin in the animal kingdom handle social unrest(n. 不安;动荡的局面)不安的状态这就是为什么我们人类有执法机构、军方和公正仲裁员像杰瑞·施普林格。

A team of anthropologists spent nearly 600 hours observing the social interactions of chimps at a Swiss zoo. And they saw the alpha male or his beta sidekick break up 69 different scuffles by running into the fray or getting up in the face of the warring parties, which were sometimes males but often females.This kind of peacekeeping is not peculiar to Swiss apes. Chimps in an English zoo, and even in the wild, exhibit similar policing. And in some cases it's a female that's the top cop.Such social intercession may have evolved to help stabilize the community, which ultimately benefits all its members. Including Chimpsky and Hutch.—Karen HopkinIntervene vi. 干涉;调停;插入premise n. 前提;上述各项;房屋连地基vt. 引出,预先提出;作为…的前提vi. 作出前提Dispute n. 辩论;争吵vt. 辩论;怀疑;阻止;抗拒vi. 争论Enforcement n. 执行,实施;强制Impartial adj. 公平的,公正的;不偏不倚的Arbitrator n. 公断人,仲裁人Jerry SpringerAlpha n. 希腊语的第一个字母beta n. 贝它(希腊字母表的第二个字母)Sidekick n. 伙伴,老朋友;插袋Scuffle n. 混战;扭打vi. 扭打;乱斗;拖着脚走路Fray n. 争论;打架;磨损处vt. 使磨损;变得令人紧张、急躁vi. 被磨损Peacekeeping adj. 维护和平的;执行停火协定的Peculiar n. 特权;特有财产adj. 特殊的;独特的;奇怪的;罕见的Intercession n. 调解;说情;仲裁Chimpsky and HutchKin n. 亲戚;家族;同族adj. 同类的;有亲属关系的;性质类似的Fruit and veggies don't just improve your diet—they could enhance your looks. A new study, done with primarily Caucasian subjects, finds that eating produce heightens red and yellow skin tones, which increases attractiveness. The work is in Public Library of Science ONE.The organic pigment s called carotenoid s provide a yellow-red color to fruit and vegetables, and when consumed, to human skin.Researchers had 35 students fill out questionnaires about how much produce they ate daily, and a spectrophotometer measured their skin color. They collected the same data three weeks later, and again after six weeks. And the more fruit and vegetables participants ate, the more vividly colored was their skin.Based on the measured color changes, the researchers created face images that other students rated for health and attractiveness. And the redder and yellower skin color from even slightly increased produce consumption was rated higher than the hue associated with a produce-poorer diet. The researchers say they need to determine if the effect also holds true for non-white people—but they expect it will. Simply put, eating healthy looks good.—Sophie BushwickCaucasian [kɔ:'keiziən] n. 白种人;高加索人adj. 白种人的;高加索的veggies详细»n. 蔬菜;素菜类;素食主义者(veggy的复数形式primarily ['praɪm(ə)rɪlɪ; praɪ'mer-] 详细»adv. 首先;主要地,根本上attractiveness [ə'træktivnis] 详细»n. 吸引力;迷惑力pigment ['pɪgm(ə)nt] 详细»n. [物][生化] 色素;颜料vt. 给…着色vi. 呈现颜色carotenoid [kə'rɔtənɔid] 详细»n. 类胡萝卜素produce [prə'djuːs] 详细»n. 农产品,产品vt. 生产;引起;创作vi. 生产,创作spectrophotometer [,spektrə(ʊ)fəʊ'tɒmɪtə] 详细»n. [光] 分光光度计rated ['reitid] 详细»v. 认为(rate的过去分词);估价adj. 额定的hue [hjuː] 详细»n. 色彩;色度;叫声Skin tone 肤色The average price for a gallon of gas in the U.S. today was nearly $3.78 per gallon. But why do we calculate fuel expenditure in dollars per gallon? Wouldn't a more realistic figure be cost per mile?The Web site used a collection of federal agency figures to determine that the average price of a gallon of gasoline in March of 1981, another high-price period, was the equivalent to $3.55 in 2012 money.But if you were driving in 1981, your car probably got lousy mileage. In 1981 the CAFE standard, that is the corporate average fuel economy requirement set by the government, was just 22 miles per gallon for passenger cars. If you actually got that mileage, you paid the 2012 equivalent of, on average, 16.1 cents to go a mile.Today, CAFE standards are up to 30.2 miles per gallon. If you actually get that mileage, with gas at $3.78, you are paying 12-and-a-half cents to go a mile. The price per gallon isn't necessarily the price of gas.—Steve Mirskyexpenditure [ɪk'spendɪtʃə; ek-] 详细»n. 支出,花费;经费,消费额realistic [rɪə'lɪstɪk] 详细»adj. 现实的;现实主义的;逼真的;实在论的lousy ['laʊzɪ] 详细»adj. 讨厌的;多虱的;污秽的;极坏的mileage ['maɪlɪdʒ] 详细»n. 英里数As voters vacillate among the contenders for the Republican nomination, it may matter less what the candidates say than how they sound when they say it. Because a new study shows that voters are more likely to prefer the candidate with the deeper voice.Previous studies have suggested that voters might go for the baritone over the tenor. But those experiments used recordings of former U.S. presidents, which meant that volunteer listeners might have recognized the speakers and voted along party lines.In this study, researchers played subjects a pair of anonymous voices and asked which they would elect: “I urge you to vote for me this November”or “I urge you to vote for me this November.”Okay, the recordings they used were no doubt less comical. But voters went with the overnight DJ hands down, results that appear in the Proceedings of the Royal Society B. [Casey A. Klofstad, Rindy C. Anderson and Susan Peters, "Sounds like a winner: voice pitch influences perception of leadership capacity in both men and women"]So why do we tend to elect Orson Welles over Pee Wee Herman? Deep voices may strike some primal chord, giving the impression of strength and competence. So candidates take heed: it’s great to wave the stars and stripes, but what’s really key is your set of pipe s.vacillate ['væsɪleɪt] 详细»vi. 犹豫;踌躇;摇摆contender [kən'tɛndɚ] 详细»n. 竞争者;争夺者contender [kən'tɛndɚ] 详细»n. 竞争者;争夺者baritone ['bærɪtəʊn] 详细»n. 男中音;男中音歌手adj. 男中音的tenor ['tenə] 详细»n. (生活等的)一般趋向;进程;(文章等的)大意,要旨;思路adj. 【音乐】;男高音的;次中音部的party line.1. 电话合用线2. [美国英语](宅地、土地的)分界线3. 政党(尤指共产党)的政治路线,政党的政策anonymous [ə'nɒnɪməs] 详细»adj. 匿名的,无名的;无个性特征的comical ['kɒmɪk(ə)l] 详细»adj. 滑稽的,好笑的primal ['praɪm(ə)l] 详细»n. 被压抑童年情绪的释放adj. 原始的;主要的;最初的vt. 释放(被压抑的童年情绪)chord [kɔːd] 详细»n. 弦;和弦competence ['kɒmpɪt(ə)ns] 详细»n. 能力,胜任;权限;作证能力;足以过舒适生活的收入heed [hi:d] 详细»vi. 注意,留心n. 注意到;留心到vt. 注意,留心pipe [paɪp] 详细»n. 管;烟斗;笛vt. 用管道输送;尖声唱;用管乐器演奏vi. 吹笛;尖叫2012-03-16 13:47:42Every year, about 10 million tons of paper winds up in American landfills and incinerators, which is not only wasteful but adds CO2 to the atmosphere. Recycling helps, but even that material has to be repulped and paper-ized before you can use it to print out that recipe you’ll never make. But what if you could wipe the page clean and use it again?Light amplification by stimulated emission of radiation to the rescue. A new study shows that laser light can erase the toner from a piece of printed paper. The approach appears in the Proceedings of the Royal Society A.Taking a page from the art-restoration handbook, scientists sampled a variety of light sources to see if any could be used to strip the ink from laser-printed documents without damaging or discoloring the paper. UV and infrared were too harsh. But a bright green laser applied in 4 nanosecond pulses vaporizes the print, leaving paper that looks as good as new.Such unprinters will probably run about 30,000 bucks, so they probably won’t catchon for home use. But people in the recycling world might find that the green laser fits the bill—for making paper that’s really green.—Karen Hopkinlandfills详细»填埋网络释义┈垃圾填埋垃圾填埋场incinerators详细»焚化炉repulp详细»n. 重新制浆emission [ɪ'mɪʃ(ə)n] 详细»n. (光、热等的)发射,散发;喷射;发行rescue ['reskjuː] 详细»n. 营救;援救;解救vt. 营救;援救toner ['təʊnə] 详细»n. 调色剂,增色剂;色粉restoration [restə'reɪʃ(ə)n] 详细»n. 恢复;复位;王政复辟;归还strip [strɪp] 详细»n. 带;条状;脱衣舞vt. 剥夺;剥去;脱去衣服vi. 脱去衣服nanosecond ['nænə(ʊ)sekənd] 详细»n. 纳秒;十亿分之一秒vaporize ['veɪpəraɪz] 详细»vi. 蒸发vt. 使…蒸发201203172012-03-17 13:48:45You know the scene—it’s a Friday night, and your date just canceled. You’re bummed, maybe a little hurt. You think now might be a good time for a beer, maybe a bourbon. And you have good company: fruit flies. Turns out that sexually deprived male fruit flies hit the bottle more frequently than sexually satisfied ones.Researchers placed one group of males repeatedly in a container with females who’d already mated. Those females were no longer receptive to sex. So the males learned to stop trying.The scientists placed another group with virgin females, who were receptive. Then they offered the two groups of males a choice of food. One choice was supplemented with ethanol. And the sexually frustrated flies dove for the drink in significantly greater numbers.This behavior was also predicted by a particular neuropeptide in the flies’ brains. The sexually deprived flies had a low level of the molecule. The scientists found they could moderate the flies’ alcohol-seeking behavior just by upping this molecule. The research was published in the journal Science. [G. Shohat-Ophir et al., "Sexual Deprivation Increases Ethanol Intake in Drosophila"]The finding could help explain how addiction may be determined both by the brain and by social conditions—especially when those are tough to swallow.—Cynthia Graberbum [bʌm] 详细»n. 流浪汉;屁股;狂欢作乐;能力差的人;嗡嗡声;执达员(等于bumbailiff)vi. 流浪;靠乞讨过活;发嗡嗡声vt. 乞讨;闲荡adj. 无价值的;劣质的;很不愉快的Bourbon ['bɜːb(ə)n; 'bʊə-] 详细»n. (法国的)波旁皇族;波本波旁波本威士忌repeatedly [rɪ'pitɪdli] 详细»adv. 反复地;再三地;屡次地receptive [rɪ'septɪv] 详细»adj. 善于接受的;能容纳的virgin ['vɜːdʒɪn] 详细»n. 处女adj. 处女的;纯洁的;未经利用的,处于原始状态的supplemented详细»v. 增补,补充(supplement的过去分词)ethanol ['eθənɒl] 详细»n. [有化] 乙醇,[有化] 酒精dove [dʌv] 详细»n. 鸽子;鸽派人士v. 潜水(dive的过去式)neuropeptide [,njuərə'peptaid] 详细»n. [生化] 神经肽moderate ['mɒd(ə)rət] 详细»adj. 稳健的,温和的;适度的,中等的;有节制的vt. 节制减轻vi. 变缓和,变弱drosophila [drɒ'sɒfɪlə] 详细»n. 果蝇;果蝇属addiction [ə'dɪkʃ(ə)n] 详细»n. 上瘾,沉溺;癖嗜20120320Scientists discover new species all the time—on the order of 15,000 a year. One of the latest additions to the tree of life is a new type of leopard frog. Which might sound unremarkable, except for where it was found: New York City.But how does a frog go unnoticed in the Big Apple? Well even experts have a hard time telling this new species from its northern and southern cousins on looks alone. But the new guy has a different croak, which raised ecologists' suspicions. So they tracked down four leopard frog populations with the unique call—including one within view of the Statue of Liberty—and took DNA samples.As they suspected, the odd croakers weren't southern or northern leopard frogs, or even a mix. They had a genetic ancestry of their own—earning them new species status. Those results appear in the journal Molecular Phylogenetics and Evolution. [Catherine E. Newman et al, A new species of leopard frog (Anura: Ranidae) from the urban northeastern US]The frogs are tough New Yorkers—the center of their range appears to be Yankee Stadium. But the researchers say that the urban amphibians face threats like pesticides and infectious diseases. Not to mention real-life games of Frogger.—Christopher Intagliataleopard frog详细»【动物】豹蛙(Rana pipiens,产于北美洲的绿色青蛙)croak [krəʊk] 详细»n. 呱呱叫声;低沉沙哑的说话声vt. 用嘶哑的声音说;死亡vi. 呱呱地叫;发牢骚;死croaker ['krəʊkə] 详细»n. 嘎声的人;喊冤者,鸣冤者ancestry ['ænsestrɪ] 详细»n. 祖先;血统phylogenetics [,failədʒi'netiks] 详细»n. [进化] 系统发生学;种系遗传学amphibians详细»n. 两栖动物;[古生] 两栖类pesticide ['pestɪsaɪd] 详细»n. 杀虫剂20120321Is the attempt to make environmentally friendly roadways doomed to wind up in the toilet? Actually, it may be the other way around. To earn a green certification, the Meador-Kansas-Ellis Trail in Bellingham, Washington, included 400 recycled commodes in the concrete.Green roads is a new rating system, developed at the University of Washington, which judges the sustainability of roads and road construction projects. Under the system, projects must incorporate11 specific features, such as dealing with waste from the construction process, as well as some optional practices, which in the case of the Meador Kansas Ellis Trail included recycling.The toilet interment helped the project win the first official Green roads nod, earning a silver certification. About 30 percent of the pavement consists of recycled concrete and, yes, crushed-up toilets, ni cknamed ―poticrete.‖But this project’s sustainability relies on more than old throne s. The Trail’s porous concrete prevents excessive run-off; it’s illuminated with low-energy lighting; and its mere presence encourages bicycle and foot traffic. These green features mean that sustainable roadways can be more than a pipe dream.—Sophie Bushwickcommode [kə'məʊd] 详细»n. 洗脸台;便桶;衣柜sustainability [sə,stenə'bɪlɪti] 详细»n. 持续性;永续性;能维持性incorporate [ɪn'kɔːpəreɪt] 详细»vt. 包含,吸收;体现;把……合并adj. 合并的;一体化的;组成公司的vi. 合并;混合;组成公司interment [ɪn'tɜːm(ə)nt] 详细»n. 葬礼;埋葬pavement ['peɪvm(ə)nt] 详细»n. 人行道throne [θrəʊn] 详细»n. 王座;君主;王权vt. 使登王位vi. 登上王座mere [mɪə] 详细»n. 小湖;池塘adj. 仅仅的;只不过的20120322When you hear Western music, you generally get the emotional tone. A major key is happy. (Music plays.) A minor one? That’s sad. (Music plays.)And spoken voices reflect this tonality. Here’s someone sounding positive: ―I don’t know who made this cake but it is fantastic!‖ And down on his luck: ―The papers finalizing the divorce came today.‖The researchers wanted to know: are these sounds international? So they turned to classical music from southern India. Here’s one that represents joy. (Raga plays.) Another displays grief and sadness. (Raga plays.) As for the spoken word, I bet you can tell the positive speaker (woman speaks) from the negative one (woman speaks).The researchers analyzed music and 20 native Tamil and American English speakers for a variety of sound and tone parameters. The authors say that certain emotional tones seem to be cross-cultura l, and that music mimics voice. The research was published in the journal Public Library of Science One. [Daniel Liu Bowling et al, Expression of Emotion in Eastern and Western Music Mirrors V ocalization] /article/info%3Adoi%2F10.1371%2Fjournal.pone.0031942So we may often be able to understand the moods of a culture in music and even in speech – without understanding a word.—Cynthia Grabertonality [tə(ʊ)'nælɪtɪ] 详细»n. 音调;色调finalize ['fainəlaiz] 详细»vt. 完成;使结束vi. 把最后定下来;定案grief [griːf] 详细»n. 悲痛;忧伤;不幸tamil ['tæmil, 'tʌ-] 详细»n. 泰米尔人;泰米尔语adj. 泰米尔人的;坦米尔语的parameters详细»n. 参数;参量(parameter的复数)cross-cultural [,krɔ:s'kʌltʃərəl] 详细»adj. 跨文化的;交叉文化的。

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