高中数学1.3.1圆与四边形课件北师大版选修4-1

1、-* *-3 3圆与四边形圆与四边形-* *-3 3.1 1圆内接四边形ZHISHI SHULI知识梳理ZHONGNAN JVJIAO重难聚焦SUITANGYANLIAN随堂演练DIANLI TOUXI典例透析MUBIAODAOHANG目标导航1.了解圆内接四边形的概念,掌握圆内接四边形的性质定理及其推论.2.理解并掌握圆内接四边形的判定定理及其推论.ZHISHI SHULI知识梳理ZHONGNAN JVJIAO重难聚焦SUITANGYANLIAN随堂演练DIANLI TOUXI典例透析MUBIAODAOHANG目标导航1234ZHISHI SHULI知识梳理ZHONGNAN JVJIAO重难

2、聚焦SUITANGYANLIAN随堂演练DIANLI TOUXI典例透析MUBIAODAOHANG目标导航1234ZHISHI SHULI知识梳理ZHONGNAN JVJIAO重难聚焦SUITANGYANLIAN随堂演练DIANLI TOUXI典例透析MUBIAODAOHANG目标导航1234【做一做1】 四边形ABCD内接于O,A=25,则C等于().A.25B.75C.115 D.155解析:四边形ABCD内接于O,A+C=180.又A=25,C=180-A=155.答案:DZHISHI SHULI知识梳理ZHONGNAN JVJIAO重难聚焦SUITANGYANLIAN随堂演练DIANL

3、I TOUXI典例透析MUBIAODAOHANG目标导航1234ZHISHI SHULI知识梳理ZHONGNAN JVJIAO重难聚焦SUITANGYANLIAN随堂演练DIANLI TOUXI典例透析MUBIAODAOHANG目标导航1234ZHISHI SHULI知识梳理ZHONGNAN JVJIAO重难聚焦SUITANGYANLIAN随堂演练DIANLI TOUXI典例透析MUBIAODAOHANG目标导航1234ZHISHI SHULI知识梳理ZHONGNAN JVJIAO重难聚焦SUITANGYANLIAN随堂演练DIANLI TOUXI典例透析MUBIAODAOHANG目标导航12

4、34ZHISHI SHULI知识梳理ZHONGNAN JVJIAO重难聚焦SUITANGYANLIAN随堂演练DIANLI TOUXI典例透析MUBIAODAOHANG目标导航1234【做一做3】 下列四边形的四个顶点共圆的是().A.梯形 B.矩形C.平行四边形D.菱形答案:BZHISHI SHULI知识梳理ZHONGNAN JVJIAO重难聚焦SUITANGYANLIAN随堂演练DIANLI TOUXI典例透析MUBIAODAOHANG目标导航1243ZHISHI SHULI知识梳理ZHONGNAN JVJIAO重难聚焦SUITANGYANLIAN随堂演练DIANLI TOUXI典例透析M

5、UBIAODAOHANG目标导航1243ZHISHI SHULI知识梳理ZHONGNAN JVJIAO重难聚焦SUITANGYANLIAN随堂演练DIANLI TOUXI典例透析MUBIAODAOHANG目标导航反证法剖析:反证法是一种论证方式,假设在原命题的条件下,结论不成立,然后推出一个明显矛盾的结果,从而说明假设不成立,原命题得证.如教材中,证明四点共圆的判定定理时,所使用的方法就是反证法.据说,古希腊三个哲学家,由于争论和天气炎热感到疲倦了,就在花园里的一棵大树下躺下来休息,结果都睡着了.这时一个爱开玩笑的人用炭涂黑了他们的前额.三个人醒来以后,彼此看了看,都笑了起来.但这并没引起他们

6、之中任何一个人的担心,因为每个人都以为是其他两人在互相取笑.这时其中有一个人突然不笑了,因为他发觉自己的前额也被涂黑了.那么他是怎样觉察到的呢?ZHISHI SHULI知识梳理ZHONGNAN JVJIAO重难聚焦SUITANGYANLIAN随堂演练DIANLI TOUXI典例透析MUBIAODAOHANG目标导航为了方便,用甲、乙、丙分别代表三个哲学家,并不妨设甲已发觉自己的脸被涂黑了.那么甲这样想:“我们三个人都可以认为自己的脸没被涂黑,如果我的脸没被涂黑,那么乙能看到(当然对于丙也是一样),乙既然看到了我的脸没被涂黑,同时他又认为他的脸也没被涂黑,那么乙就应该对丙的发笑而感到奇怪.因为在

7、这种情况下(甲、乙的脸都是干净的),丙是没有可笑的理由了.然而现在的事实是乙对丙的发笑并不感到奇怪,可见乙是在认为丙在笑我.由此可知,我的脸也被涂黑了.”这里应着重指出的是,甲并没有直接看到自己的脸是否被涂黑了,他是根据乙、丙两人的表情进行分析、思考,而说明了自己的脸被涂黑了.简单地说,甲是通过说明脸被涂黑了的反面没被涂黑是错误的,从而觉察了自己的脸被涂黑了.因此这是一种间接的证明方法.像这样,为了说明某一个结论是正确的,但不从正面直接说明,而是通过说明它的反面是错误的,从而断定它本身是正确的方法,就是反证法.ZHISHI SHULI知识梳理ZHONGNAN JVJIAO重难聚焦SUITANG

8、YANLIAN随堂演练DIANLI TOUXI典例透析MUBIAODAOHANG目标导航题型一题型二ZHISHI SHULI知识梳理ZHONGNAN JVJIAO重难聚焦SUITANGYANLIAN随堂演练DIANLI TOUXI典例透析MUBIAODAOHANG目标导航题型一题型二证明:EG平分AED,AEG=CEF.四边形ABCD是O的内接四边形,FCE=GAE.DGF=GAE+AEG,CFG=FCE+CEF,CFG=DGF.ZHISHI SHULI知识梳理ZHONGNAN JVJIAO重难聚焦SUITANGYANLIAN随堂演练DIANLI TOUXI典例透析MUBIAODAOHANG目

9、标导航题型一题型二ZHISHI SHULI知识梳理ZHONGNAN JVJIAO重难聚焦SUITANGYANLIAN随堂演练DIANLI TOUXI典例透析MUBIAODAOHANG目标导航题型一题型二ZHISHI SHULI知识梳理ZHONGNAN JVJIAO重难聚焦SUITANGYANLIAN随堂演练DIANLI TOUXI典例透析MUBIAODAOHANG目标导航题型一题型二ZHISHI SHULI知识梳理ZHONGNAN JVJIAO重难聚焦SUITANGYANLIAN随堂演练DIANLI TOUXI典例透析MUBIAODAOHANG目标导航题型一题型二证明:连接PF,如图所示.AP

10、BC,F为AC的中点,PF是RtAPC斜边上的中线.PF=FC.FPC=C.E,F,D分别为AB,AC,BC的中点,EFCD,EDFC.四边形EDCF为平行四边形.FED=C.FPC=FED.E,D,P,F四点共圆.ZHISHI SHULI知识梳理ZHONGNAN JVJIAO重难聚焦SUITANGYANLIAN随堂演练DIANLI TOUXI典例透析MUBIAODAOHANG目标导航题型一题型二ZHISHI SHULI知识梳理ZHONGNAN JVJIAO重难聚焦SUITANGYANLIAN随堂演练DIANLI TOUXI典例透析MUBIAODAOHANG目标导航题型一题型二【变式训练2】

11、在锐角三角形ABC中,AD是BC边上的高,DEAB,DFAC,E,F是垂足,求证:E,B,C,F四点共圆.证明:如图所示,连接EF.DEAB,DFAC,A,E,D,F四点共圆,DEF=DAF.DEF+ACD=DAF+ACD=90,BEF+ACD=180.B,E,F,C四点共圆.ZHISHI SHULI知识梳理ZHONGNAN JVJIAO重难聚焦SUITANGYANLIAN随堂演练DIANLI TOUXI典例透析MUBIAODAOHANG目标导航1 2 3 4 5ZHISHI SHULI知识梳理ZHONGNAN JVJIAO重难聚焦SUITANGYANLIAN随堂演练DIANLI TOUXI典

12、例透析MUBIAODAOHANG目标导航1 2 3 4 52四边形ABCD内接于O,ABC=237,则D的度数为().A.72B.100 C.110 D.120解析:圆的内接四边形的对角互补,A+C=180.ABC=237,A=40,B=60,C=140.B+D=180,D=180-60=120.答案:DZHISHI SHULI知识梳理ZHONGNAN JVJIAO重难聚焦SUITANGYANLIAN随堂演练DIANLI TOUXI典例透析MUBIAODAOHANG目标导航1 2 3 4 5ZHISHI SHULI知识梳理ZHONGNAN JVJIAO重难聚焦SUITANGYANLIAN随堂演

13、练DIANLI TOUXI典例透析MUBIAODAOHANG目标导航1 2 3 4 5解析:FPBC,FQAC,FPC+FQC=90+90=180.四边形FPCQ内接于圆.CQP=CFP.A=60,ACB=70,B=50.PFB=90-B=40.又CF是ABC的边AB上的高,CFP=90-PFB=50.CQP=CFP=50.答案:50ZHISHI SHULI知识梳理ZHONGNAN JVJIAO重难聚焦SUITANGYANLIAN随堂演练DIANLI TOUXI典例透析MUBIAODAOHANG目标导航1 2 3 4 5ZHISHI SHULIZHISHI SHULIZHISHI SHULIZ

14、HISHI SHULI知识梳理知识梳理知识梳理知识梳理ZHONGNAN JVJIAOZHONGNAN JVJIAOZHONGNAN JVJIAOZHONGNAN JVJIAO重难聚焦重难聚焦重难聚焦重难聚焦SUITANGYANLIANSUITANGYANLIANSUITANGYANLIANSUITANGYANLIAN随堂演练随堂演练随堂演练随堂演练DIANLI TOUXIDIANLI TOUXIDIANLI TOUXIDIANLI TOUXI典例透析典例透析典例透析典例透析MUBIAODAOHANGMUBIAODAOHANGMUBIAODAOHANGMUBIAODAOHANG目标导航目标导航目标导航目标导航1 2 3 4 5解析:AB为O的直径,ACB=90.ABC=90-BAC=90-20=70.又四边形ABCD内接于O,ABC+ADC=180.ADC=180-ABC=180-70=110.则在ADC