1、24.1.3 弧、弦、圆心角核心目标.21课前预习.3课堂导学.45课后巩固.能力培优.核心目标 了解弧、弦、圆心角之间的关系，并会利用这些关系进行简单的证明和计算课前预习1顶点在_的角叫圆心角2在同圆或等圆中，相等的圆心角所对的_相等，所对的_也相等3在同圆或等圆中，如果两条弧相等，那么它们所对的_相等，所对的_相等4在同圆或等圆中，如果两条弦相等，那么它们所对的_相等，所对的_相等弦圆心弧弦圆心角圆心角弧课堂导学【例题】如右图，以ABCD的顶点A为圆心，AB为半径作A，A交AD、BC于E、F，延长BA交A于G.求证：GEEF.(【解析】要证GEEF，由弧、弦、圆心角的关系定理知只需证GE与
2、EF所对的圆心角相等或弦GEEF.(课堂导学【答案】证明：连接AF.ABAF，ABFAFB，ABCD中，ADBC，GAEABF，EAFAFB，GAEEAF，GEEF.(【点拔】在圆中求解圆心角、弧、弦等问题时，常运用它们三者之间的等对等关系进行转化，这是解题的常用方法课堂导学对点训练1如下图，已知BD是O的直径，点A、C在O上，ABBC，AOB60，则BOC_度(2如图，在O中，ABAC，A40，则B_度(6070课堂导学3如上图，D、E分别是O的半径OA、OB上的点，CDOA，CEOB，CDCE，则AC与CB的大小关系是()AACCB BACCB CACCB D不能确定(B课堂导学4如下图，
3、已知AB、CD是O的直径，E是O上的一点，BDCE.求证：ACCE(AOCBOD，ACBD又BDCE，ACCE，ACCE(课后巩固5如下图，已知在O中，BC 是直径，ABDC，AOD 80，则ABC等于()A40 B65 C100 D105(6如上图，已知O的半径等于 1cm，AB是直径，C，D是 O上的两点，且ADDCCB,则四边形ABCD的周长等于()A4cm B5cm C6cm D7cm(BB课后巩固7如右下图，在O中，ABCD，则下列结论错误的是()AABCD BACBD CACBD DADBD(D课后巩固8如下图，在O中，CD为O的直径，ACBC，点E为OD上任意一点(不与O、D重合
4、)求证：AEBE.(ACBC，AOCBOCAODBOD，又OAOB，OEOE，得AOEBOE，AEBE(课后巩固9如下图，已知AB是O的弦，半径OC、OD与AB分别交于点E、F，且AEBF.求证：ACBD.(连接OA、OB，由OAOB得AB又AEBF，AOEBOF，AOEBOF，ACBD(课后巩固10(2017牡丹江)如下图，在O中，ACCB，CDOA于D，CEOB于E，求证：ADBE.(证明：连接OC，ACCB，AOCBOCCDOA于D,CEOB于E,CDOCEO90在COD与COE中，,CODCOE(AAS)，ODOE，AOBO，ADBE(DOCEOCCDOCEO90COCO课后巩固11如
5、下图，AB是圆O的直径，D是圆上的一点，DOB75，DC交BA的延长线于E，交半圆于C，且CEAO，求E的度数解：连结OC，如图，CEAO，而OAOC，OCEC，E1，2E12E，OCOD，D22E，BODED，E2E75，E25能力培优(1)若ACBD，求证：AMBN；12如下图，在O中，C、D是直径AB上两点，MCAB，NDAB，M，N在O上连接OM、ON，OAOB，ACBD，OCOD，RtOCMRtODN，COMDOM，AMBN(能力培优(2)若C，D分别为OA、OB的中点，试判断AMMN NB是否成立?说明你的理由(成立，理由：连接AM，MCOA，ACOC，MC垂直平分OA，AMOMO
6、A，AOM是等边三角形，AOM60，同理BON60，MON60，AOMMONBON，AMMNBN感谢聆听全文结束！再见全文结束！再见o study whether experiences during teen years would influence adult health.So they followed 171 teens,starting when the kids were just 13.They interviewed each one every year for five years，and also spoke to these teens closest friend
7、s，who provided additional information about the quality of their friendships.The same 171 people were interviewed again at ages 25,26 and 27.This time,the questions surveyed each persons overall health.When the researchers analyzed the data,they found a strong connection between a teens behavior and
8、 adult health.Teens who had close friends grew up to be the healthier adults.Whether teens held back their feelings or expressed them to close friends also influenced later health.Those who held back their feelings were more likely to be sick as adults.The connection held up even after the scientist
9、s accounted for other possible influences on health.Weight，family income and drug use were all examined.So were mental health issues，such as anxiety and depression.And in these people，such other factors did not explain adult health as well as teen friendships did.Getting along with the crowd may hav
10、e benefits,says Allen,but there are also drawbacks.Teens who are more independent tend to do better at school and work.And peer pressure may lead some kids to engage in risky behavior,such as smoking,drinking or using drugs.Dealing with it is an ongoing challenge，Allen acknowledges.“Finding the right balance is the key.Teens shouldnt lose heart for not finding this easy.”And,he adds，“Parents need to be understanding about the pressures teens face.”
