2017 2018人教版九年級(jí)中考數(shù)學(xué)總復(fù)習(xí)課件第31課時(shí) 軸對(duì)稱共17張

1、第,31,課時(shí),軸對(duì)稱,考點(diǎn),1,軸對(duì)稱圖形與軸對(duì)稱,軸對(duì)稱,圖形,如果一個(gè)平面圖形沿一條直線折疊,直線兩旁的,部分能夠互相,這個(gè)圖形叫做軸對(duì)稱圖,形,這條直線叫做,軸對(duì)稱,把一個(gè)圖形沿著某一條直線折疊,如果它能夠與,另一個(gè)圖形重合,那么就說(shuō)這兩個(gè)圖形關(guān)于這條,直線,這條直線叫做,折疊,后重合的點(diǎn)叫做,重合,對(duì)稱軸,對(duì)稱,對(duì)稱軸,對(duì)稱點(diǎn),軸對(duì)稱圖,形與軸對(duì),稱的區(qū)別,軸對(duì)稱圖形是指一個(gè)圖形所具有對(duì)稱關(guān)系,而軸對(duì)稱是指兩個(gè)圖形的對(duì)稱關(guān)系,把成軸對(duì)稱的兩個(gè)圖形看成一個(gè)整體,它就,是一個(gè),圖形,把一個(gè)軸對(duì)稱圖,形沿對(duì)稱軸分成兩個(gè)圖形,這兩個(gè)圖形關(guān)于,這條軸對(duì)稱,軸對(duì)稱的,性,質(zhì),如果兩個(gè)圖形關(guān)于某條

2、直線對(duì)稱,那么對(duì)稱,軸是任何一對(duì)對(duì)應(yīng)點(diǎn)所連線段的,軸對(duì)稱圖形的對(duì)稱軸,是任何一對(duì)對(duì)應(yīng)點(diǎn)所,連線段的,軸對(duì)稱,垂直平分線,垂直平分線,1,教材原題,如圖,利用關(guān)于坐標(biāo)軸對(duì)稱的點(diǎn),的坐標(biāo)的特點(diǎn),分別畫出,ABC,關(guān)于,x,軸對(duì),稱的,A,B,C,和關(guān)于,y,軸對(duì)稱的,A,B,C,1,2,3,4,1,2,3,4,1,2,3,1,2,x,y,O,4,1,A,1,1,B,3,2,C,A,C,B,C,A,B,2,2017,瀘州中考,已知點(diǎn),1,A,a,與點(diǎn),4,B,b,關(guān)于,y,軸對(duì)稱,則,a,b,的值為,A,5,B,3,C,3,D,5,D,3,變式,下列圖形中,一定是軸對(duì)稱圖形的是,A,B,C,D,角,

3、銳角三角形,直角三角形,平行四邊形,A,4,變式,PQR,在平面直角坐標(biāo)系中的位置如圖所示,1,作,PQR,關(guān)于直線,m,直線,m,上各點(diǎn)的橫坐標(biāo),都為,1,對(duì)稱圖形,P,Q,R,則點(diǎn),M,x,y,關(guān)于直,線,m,的對(duì)稱點(diǎn)的坐標(biāo)為,1,2,3,4,1,2,3,4,1,2,3,4,1,2,5,5,3,4,6,5,5,6,m,y,Q,P,O,R,x,n,7,2,x,y,P,Q,R,2,作,PQR,關(guān)于直線,n,直線,n,上各點(diǎn)的縱坐,標(biāo),都,為,1,的,對(duì)稱,圖,形,P,Q,R,則,點(diǎn),M,x,y,關(guān)于直線,n,的對(duì)稱點(diǎn)的坐標(biāo)為,1,2,3,4,1,2,3,4,1,2,3,4,1,2,5,5,3,

4、4,6,5,5,6,m,y,Q,P,O,R,x,n,7,R,P,Q,2,x,y,考點(diǎn),2,線段的垂直平分線,定義,經(jīng)過(guò)線段,并且,于這條線段的直,線,叫做這條線段的垂直平分線,性質(zhì),線段垂直平分線上的點(diǎn)與這條線段兩個(gè),的距離相等,判定,與一條線段的兩個(gè),距離相等的點(diǎn),在這條線段的垂直平分線上,拓展,三角形三條邊的垂直平分線相交于一點(diǎn),并且這,一點(diǎn)到三個(gè)頂點(diǎn)的距離相等,中點(diǎn),垂直,端點(diǎn),端點(diǎn),5,教材原題,如圖,在,ABC,中,邊,AB,BC,的,垂直平分線交于點(diǎn),P,1,求證,PA,PB,PC,A,B,C,P,證明,點(diǎn),P,是,AB,的垂直平分線,上的點(diǎn),PA,PB,同理,PB,PC,PA,P

5、B,PC,2,點(diǎn),P,是否也在邊,AC,的垂直平分線上,由此,你還能得出什么結(jié)論,A,B,C,P,答,點(diǎn),P,也在邊,AC,的垂直平分線上,由此可知,三角形三條邊的垂直平分線相交,于一點(diǎn),6,2017,宜昌中考,如圖,在,AEF,中,尺規(guī)作圖如下,分別以點(diǎn),E,點(diǎn),F,為圓心,大于,1,2,EF,的長(zhǎng)為半徑作弧,兩弧相交于,G,H,兩點(diǎn),作直線,GH,交,EF,于點(diǎn),O,連接,AO,則下列結(jié)論正確的是,A,AO,平分,EAF,B,AO,垂直平分,EF,C,GH,垂直平分,EF,D,GH,平分,AF,F,A,G,H,E,O,C,7,變式,如圖,在,ABC,中,FD,FE,分別垂直平分,AC,和,

6、BC,分別交,AB,于,M,N,連接,CM,CN,1,若,CMN,的周長(zhǎng)為,15,cm,求,AB,的長(zhǎng),B,C,N,D,A,F,M,E,解,FD,FE,分別垂直平分,AC,和,BC,AM,CM,BN,CN,CMN,的周長(zhǎng),15,CM,CN,MN,15,AM,BN,MN,15(cm,AB,2,若,70,F,o,求,MCN,的度數(shù),B,C,N,D,A,F,M,E,解,FD,FE,分別垂直平分,AC,和,BC,90,CDF,CEF,o,360,ACB,CDF,CEF,F,o,110,o,180,70,A,B,ACB,o,o,又,AM,CM,BN,CN,ACM,A,BCN,B,70,ACM,BCN,A

7、,B,o,MCN,ACB,ACM,BCN,40,8,教材原題,如圖,要把一塊三角形的土地均勻分給甲,乙、丙三家農(nóng)戶,如果,90,C,o,30,B,o,要使這三,家農(nóng)戶所得土地的大小,形狀都相同,請(qǐng)你試著分一分,在圖上畫出來(lái),A,B,C,答,作,BAC,的平分線,AD,再作,DE,AB,于,E,則,ACD,AED,BED,或作邊,AB,的垂直平分線交,AB,于,E,交,BC,于,D,連接,AD,D,E,9,2017,揚(yáng)州中考,如圖,把等邊,ABC,沿著,DE,折疊,使點(diǎn),A,恰好落在,BC,邊上的點(diǎn),P,處,且,DP,BC,若,4,BP,則,EC,P,A,B,C,D,E,2,3,2,10,變式,如圖,在一張矩形紙片,ABCD,中,4cm,AD,點(diǎn),E,F,分別是,CD,和,AB,的中點(diǎn),現(xiàn)將這張紙片折疊,使點(diǎn),B,落在,EF,上的點(diǎn),G,處,折痕為,AH,若,HG,延長(zhǎng)線恰好經(jīng)過(guò)點(diǎn),D,求,CD,的長(zhǎng),B,C,F,A,D,E,G,H,解,點(diǎn),E,F,分別是,CD,和,AB,的中點(diǎn),EF,BC,DG,DE,EC,GH,DG