高中數(shù)學(xué)1.3.1圓與四邊形課件北師大版選修4-1

1、-* *-3 3圓與四邊形圓與四邊形-* *-3 3.1 1圓內(nèi)接四邊形ZHISHI SHULI知識(shí)梳理ZHONGNAN JVJIAO重難聚焦SUITANGYANLIAN隨堂演練DIANLI TOUXI典例透析MUBIAODAOHANG目標(biāo)導(dǎo)航1.了解圓內(nèi)接四邊形的概念,掌握?qǐng)A內(nèi)接四邊形的性質(zhì)定理及其推論.2.理解并掌握?qǐng)A內(nèi)接四邊形的判定定理及其推論.ZHISHI SHULI知識(shí)梳理ZHONGNAN JVJIAO重難聚焦SUITANGYANLIAN隨堂演練DIANLI TOUXI典例透析MUBIAODAOHANG目標(biāo)導(dǎo)航1234ZHISHI SHULI知識(shí)梳理ZHONGNAN JVJIAO重難

2、聚焦SUITANGYANLIAN隨堂演練DIANLI TOUXI典例透析MUBIAODAOHANG目標(biāo)導(dǎo)航1234ZHISHI SHULI知識(shí)梳理ZHONGNAN JVJIAO重難聚焦SUITANGYANLIAN隨堂演練DIANLI TOUXI典例透析MUBIAODAOHANG目標(biāo)導(dǎo)航1234【做一做1】 四邊形ABCD內(nèi)接于O,A=25,則C等于().A.25B.75C.115 D.155解析:四邊形ABCD內(nèi)接于O,A+C=180.又A=25,C=180-A=155.答案:DZHISHI SHULI知識(shí)梳理ZHONGNAN JVJIAO重難聚焦SUITANGYANLIAN隨堂演練DIANL

3、I TOUXI典例透析MUBIAODAOHANG目標(biāo)導(dǎo)航1234ZHISHI SHULI知識(shí)梳理ZHONGNAN JVJIAO重難聚焦SUITANGYANLIAN隨堂演練DIANLI TOUXI典例透析MUBIAODAOHANG目標(biāo)導(dǎo)航1234ZHISHI SHULI知識(shí)梳理ZHONGNAN JVJIAO重難聚焦SUITANGYANLIAN隨堂演練DIANLI TOUXI典例透析MUBIAODAOHANG目標(biāo)導(dǎo)航1234ZHISHI SHULI知識(shí)梳理ZHONGNAN JVJIAO重難聚焦SUITANGYANLIAN隨堂演練DIANLI TOUXI典例透析MUBIAODAOHANG目標(biāo)導(dǎo)航12

4、34ZHISHI SHULI知識(shí)梳理ZHONGNAN JVJIAO重難聚焦SUITANGYANLIAN隨堂演練DIANLI TOUXI典例透析MUBIAODAOHANG目標(biāo)導(dǎo)航1234【做一做3】 下列四邊形的四個(gè)頂點(diǎn)共圓的是().A.梯形 B.矩形C.平行四邊形D.菱形答案:BZHISHI SHULI知識(shí)梳理ZHONGNAN JVJIAO重難聚焦SUITANGYANLIAN隨堂演練DIANLI TOUXI典例透析MUBIAODAOHANG目標(biāo)導(dǎo)航1243ZHISHI SHULI知識(shí)梳理ZHONGNAN JVJIAO重難聚焦SUITANGYANLIAN隨堂演練DIANLI TOUXI典例透析M

5、UBIAODAOHANG目標(biāo)導(dǎo)航1243ZHISHI SHULI知識(shí)梳理ZHONGNAN JVJIAO重難聚焦SUITANGYANLIAN隨堂演練DIANLI TOUXI典例透析MUBIAODAOHANG目標(biāo)導(dǎo)航反證法剖析:反證法是一種論證方式,假設(shè)在原命題的條件下,結(jié)論不成立,然后推出一個(gè)明顯矛盾的結(jié)果,從而說(shuō)明假設(shè)不成立,原命題得證.如教材中,證明四點(diǎn)共圓的判定定理時(shí),所使用的方法就是反證法.據(jù)說(shuō),古希臘三個(gè)哲學(xué)家,由于爭(zhēng)論和天氣炎熱感到疲倦了,就在花園里的一棵大樹(shù)下躺下來(lái)休息,結(jié)果都睡著了.這時(shí)一個(gè)愛(ài)開(kāi)玩笑的人用炭涂黑了他們的前額.三個(gè)人醒來(lái)以后,彼此看了看,都笑了起來(lái).但這并沒(méi)引起他們

6、之中任何一個(gè)人的擔(dān)心,因?yàn)槊總€(gè)人都以為是其他兩人在互相取笑.這時(shí)其中有一個(gè)人突然不笑了,因?yàn)樗l(fā)覺(jué)自己的前額也被涂黑了.那么他是怎樣覺(jué)察到的呢?ZHISHI SHULI知識(shí)梳理ZHONGNAN JVJIAO重難聚焦SUITANGYANLIAN隨堂演練DIANLI TOUXI典例透析MUBIAODAOHANG目標(biāo)導(dǎo)航為了方便,用甲、乙、丙分別代表三個(gè)哲學(xué)家,并不妨設(shè)甲已發(fā)覺(jué)自己的臉被涂黑了.那么甲這樣想:“我們?nèi)齻€(gè)人都可以認(rèn)為自己的臉沒(méi)被涂黑,如果我的臉沒(méi)被涂黑,那么乙能看到(當(dāng)然對(duì)于丙也是一樣),乙既然看到了我的臉沒(méi)被涂黑,同時(shí)他又認(rèn)為他的臉也沒(méi)被涂黑,那么乙就應(yīng)該對(duì)丙的發(fā)笑而感到奇怪.因?yàn)樵?/p>

7、這種情況下(甲、乙的臉都是干凈的),丙是沒(méi)有可笑的理由了.然而現(xiàn)在的事實(shí)是乙對(duì)丙的發(fā)笑并不感到奇怪,可見(jiàn)乙是在認(rèn)為丙在笑我.由此可知,我的臉也被涂黑了.”這里應(yīng)著重指出的是,甲并沒(méi)有直接看到自己的臉是否被涂黑了,他是根據(jù)乙、丙兩人的表情進(jìn)行分析、思考,而說(shuō)明了自己的臉被涂黑了.簡(jiǎn)單地說(shuō),甲是通過(guò)說(shuō)明臉被涂黑了的反面沒(méi)被涂黑是錯(cuò)誤的,從而覺(jué)察了自己的臉被涂黑了.因此這是一種間接的證明方法.像這樣,為了說(shuō)明某一個(gè)結(jié)論是正確的,但不從正面直接說(shuō)明,而是通過(guò)說(shuō)明它的反面是錯(cuò)誤的,從而斷定它本身是正確的方法,就是反證法.ZHISHI SHULI知識(shí)梳理ZHONGNAN JVJIAO重難聚焦SUITANG

8、YANLIAN隨堂演練DIANLI TOUXI典例透析MUBIAODAOHANG目標(biāo)導(dǎo)航題型一題型二ZHISHI SHULI知識(shí)梳理ZHONGNAN JVJIAO重難聚焦SUITANGYANLIAN隨堂演練DIANLI TOUXI典例透析MUBIAODAOHANG目標(biāo)導(dǎo)航題型一題型二證明:EG平分AED,AEG=CEF.四邊形ABCD是O的內(nèi)接四邊形,FCE=GAE.DGF=GAE+AEG,CFG=FCE+CEF,CFG=DGF.ZHISHI SHULI知識(shí)梳理ZHONGNAN JVJIAO重難聚焦SUITANGYANLIAN隨堂演練DIANLI TOUXI典例透析MUBIAODAOHANG目

9、標(biāo)導(dǎo)航題型一題型二ZHISHI SHULI知識(shí)梳理ZHONGNAN JVJIAO重難聚焦SUITANGYANLIAN隨堂演練DIANLI TOUXI典例透析MUBIAODAOHANG目標(biāo)導(dǎo)航題型一題型二ZHISHI SHULI知識(shí)梳理ZHONGNAN JVJIAO重難聚焦SUITANGYANLIAN隨堂演練DIANLI TOUXI典例透析MUBIAODAOHANG目標(biāo)導(dǎo)航題型一題型二ZHISHI SHULI知識(shí)梳理ZHONGNAN JVJIAO重難聚焦SUITANGYANLIAN隨堂演練DIANLI TOUXI典例透析MUBIAODAOHANG目標(biāo)導(dǎo)航題型一題型二證明:連接PF,如圖所示.AP

10、BC,F為AC的中點(diǎn),PF是RtAPC斜邊上的中線.PF=FC.FPC=C.E,F,D分別為AB,AC,BC的中點(diǎn),EFCD,EDFC.四邊形EDCF為平行四邊形.FED=C.FPC=FED.E,D,P,F四點(diǎn)共圓.ZHISHI SHULI知識(shí)梳理ZHONGNAN JVJIAO重難聚焦SUITANGYANLIAN隨堂演練DIANLI TOUXI典例透析MUBIAODAOHANG目標(biāo)導(dǎo)航題型一題型二ZHISHI SHULI知識(shí)梳理ZHONGNAN JVJIAO重難聚焦SUITANGYANLIAN隨堂演練DIANLI TOUXI典例透析MUBIAODAOHANG目標(biāo)導(dǎo)航題型一題型二【變式訓(xùn)練2】

11、在銳角三角形ABC中,AD是BC邊上的高,DEAB,DFAC,E,F是垂足,求證:E,B,C,F四點(diǎn)共圓.證明:如圖所示,連接EF.DEAB,DFAC,A,E,D,F四點(diǎn)共圓,DEF=DAF.DEF+ACD=DAF+ACD=90,BEF+ACD=180.B,E,F,C四點(diǎn)共圓.ZHISHI SHULI知識(shí)梳理ZHONGNAN JVJIAO重難聚焦SUITANGYANLIAN隨堂演練DIANLI TOUXI典例透析MUBIAODAOHANG目標(biāo)導(dǎo)航1 2 3 4 5ZHISHI SHULI知識(shí)梳理ZHONGNAN JVJIAO重難聚焦SUITANGYANLIAN隨堂演練DIANLI TOUXI典

12、例透析MUBIAODAOHANG目標(biāo)導(dǎo)航1 2 3 4 52四邊形ABCD內(nèi)接于O,ABC=237,則D的度數(shù)為().A.72B.100 C.110 D.120解析:圓的內(nèi)接四邊形的對(duì)角互補(bǔ),A+C=180.ABC=237,A=40,B=60,C=140.B+D=180,D=180-60=120.答案:DZHISHI SHULI知識(shí)梳理ZHONGNAN JVJIAO重難聚焦SUITANGYANLIAN隨堂演練DIANLI TOUXI典例透析MUBIAODAOHANG目標(biāo)導(dǎo)航1 2 3 4 5ZHISHI SHULI知識(shí)梳理ZHONGNAN JVJIAO重難聚焦SUITANGYANLIAN隨堂演

13、練DIANLI TOUXI典例透析MUBIAODAOHANG目標(biāo)導(dǎo)航1 2 3 4 5解析:FPBC,FQAC,FPC+FQC=90+90=180.四邊形FPCQ內(nèi)接于圓.CQP=CFP.A=60,ACB=70,B=50.PFB=90-B=40.又CF是ABC的邊AB上的高,CFP=90-PFB=50.CQP=CFP=50.答案:50ZHISHI SHULI知識(shí)梳理ZHONGNAN JVJIAO重難聚焦SUITANGYANLIAN隨堂演練DIANLI TOUXI典例透析MUBIAODAOHANG目標(biāo)導(dǎo)航1 2 3 4 5ZHISHI SHULIZHISHI SHULIZHISHI SHULIZ

14、HISHI SHULI知識(shí)梳理知識(shí)梳理知識(shí)梳理知識(shí)梳理ZHONGNAN JVJIAOZHONGNAN JVJIAOZHONGNAN JVJIAOZHONGNAN JVJIAO重難聚焦重難聚焦重難聚焦重難聚焦SUITANGYANLIANSUITANGYANLIANSUITANGYANLIANSUITANGYANLIAN隨堂演練隨堂演練隨堂演練隨堂演練DIANLI TOUXIDIANLI TOUXIDIANLI TOUXIDIANLI TOUXI典例透析典例透析典例透析典例透析MUBIAODAOHANGMUBIAODAOHANGMUBIAODAOHANGMUBIAODAOHANG目標(biāo)導(dǎo)航目標(biāo)導(dǎo)航目標(biāo)導(dǎo)航目標(biāo)導(dǎo)航1 2 3 4 5解析:AB為O的直徑,ACB=90.ABC=90-BAC=90-20=70.又四邊形ABCD內(nèi)接于O,ABC+ADC=180.ADC=180-ABC=180-70=110.則在ADC