1921全等三角形--

1、能夠完全重合的兩個(gè)圖形叫做全等圖形能夠完全重合的兩個(gè)圖形叫做全等圖形.全等形包括全等形包括規(guī)則規(guī)則圖形和圖形和不規(guī)則不規(guī)則圖形全等圖形全等全等圖形全等圖形:ABCEDF例如例如能夠完全重合的能夠完全重合的兩個(gè)三角形兩個(gè)三角形, ,叫做叫做記作記作:ABCABCDEFDEF讀作讀作:ABC全等于全等于DEF互相重合的頂點(diǎn)叫互相重合的頂點(diǎn)叫對(duì)應(yīng)頂點(diǎn)對(duì)應(yīng)頂點(diǎn).互相重合的邊叫互相重合的邊叫對(duì)應(yīng)邊對(duì)應(yīng)邊.互相重合的角叫互相重合的角叫對(duì)應(yīng)角對(duì)應(yīng)角.全等三角形全等三角形全等三角形的全等三角形的對(duì)應(yīng)邊對(duì)應(yīng)邊相等，相等，全等三角形的全等三角形的對(duì)應(yīng)角對(duì)應(yīng)角相等。相等。全等三角形的全等三角形的性質(zhì)性質(zhì)ABCDEF

2、如圖如圖: ABC DEF (已知已知)AB=DE, BC=EF, AC=DF (全等三角形的對(duì)應(yīng)邊相等全等三角形的對(duì)應(yīng)邊相等)A=D, B=E, C=F (全等三角形的對(duì)應(yīng)角相等全等三角形的對(duì)應(yīng)角相等)ABCDEFABCDEF?ABCEFD注意：書(shū)寫(xiě)全等式時(shí)要求把注意：書(shū)寫(xiě)全等式時(shí)要求把對(duì)應(yīng)頂點(diǎn)對(duì)應(yīng)頂點(diǎn)字字母放在對(duì)應(yīng)的位置上。母放在對(duì)應(yīng)的位置上。ADBCEFAFBEDC 試一試：試一試： 根據(jù)圖形所提供的條件和全等式：根據(jù)圖形所提供的條件和全等式：（1）在圖上標(biāo)出所缺的字母；）在圖上標(biāo)出所缺的字母；（2）說(shuō)出它們的對(duì)應(yīng)邊和對(duì)應(yīng)角）說(shuō)出它們的對(duì)應(yīng)邊和對(duì)應(yīng)角練練1A=FDE, CBA=E, C=

3、F.ABCDEF先寫(xiě)出全等式，先寫(xiě)出全等式，ABC DEFAB=DE, BC=EF, AC=DF.練練2解解:再指出它們的對(duì)應(yīng)邊和對(duì)應(yīng)角再指出它們的對(duì)應(yīng)邊和對(duì)應(yīng)角規(guī)律一：規(guī)律一：有公共邊的，公共邊是對(duì)應(yīng)邊有公共邊的，公共邊是對(duì)應(yīng)邊ABCD先寫(xiě)出全等式，先寫(xiě)出全等式，ABC ABDAB=AB,BC=BD,BAC=BAD,練練3解解:AC=AD.ABC=ABD, C= D.再指出它們的對(duì)應(yīng)邊和對(duì)應(yīng)角再指出它們的對(duì)應(yīng)邊和對(duì)應(yīng)角先寫(xiě)出全等式，先寫(xiě)出全等式，ACODBAOC BODAO=BO,AC=BD, OC=OD.A=B,C=D, AOC= BOD.規(guī)律二：規(guī)律二：有對(duì)頂角的，對(duì)頂角是對(duì)應(yīng)角有對(duì)頂角

4、的，對(duì)頂角是對(duì)應(yīng)角練練4解解:再指出它們的對(duì)應(yīng)邊和對(duì)應(yīng)角再指出它們的對(duì)應(yīng)邊和對(duì)應(yīng)角規(guī)律三：規(guī)律三：有公共角的，公共角是對(duì)應(yīng)角有公共角的，公共角是對(duì)應(yīng)角ABCDE先寫(xiě)出全等式，先寫(xiě)出全等式，ABC ADEAB=AD,AC=AE, BC=DEA=A,B=D, ACB= AED.解解:練練5再指出它們的對(duì)應(yīng)邊和對(duì)應(yīng)角再指出它們的對(duì)應(yīng)邊和對(duì)應(yīng)角規(guī)律四：規(guī)律四：一對(duì)最長(zhǎng)的邊是對(duì)應(yīng)邊一對(duì)最長(zhǎng)的邊是對(duì)應(yīng)邊 一對(duì)最短的邊是對(duì)應(yīng)邊一對(duì)最短的邊是對(duì)應(yīng)邊ABCDE先寫(xiě)出全等式，先寫(xiě)出全等式，ABC DECAB=DE,AC=DC, BC=ECA=D, B=E, ACB= DCE.練練6再指出它們的對(duì)應(yīng)邊和對(duì)應(yīng)角再指出

5、它們的對(duì)應(yīng)邊和對(duì)應(yīng)角解解:規(guī)律五：規(guī)律五：一對(duì)最大的角是對(duì)應(yīng)角一對(duì)最大的角是對(duì)應(yīng)角 一對(duì)最小的角是對(duì)應(yīng)角一對(duì)最小的角是對(duì)應(yīng)角FDEFDEFDEBCAADEFDEFDEFDEFDEFDEFDEFDEFD先寫(xiě)出全等式，先寫(xiě)出全等式，ABC FDCAB=FD,AC=FC, BC=DCA=F, B=D, ACB= FCD.解解:再指出它們的對(duì)應(yīng)邊和對(duì)應(yīng)角再指出它們的對(duì)應(yīng)邊和對(duì)應(yīng)角練練7對(duì)應(yīng)角是對(duì)應(yīng)角是: BOF和和COE、 BFO 和和CEO、 FOB和和EOC。對(duì)應(yīng)邊是：。對(duì)應(yīng)邊是：OF和和OE、OB和和OC、BF和和CE。下列全等三角形的對(duì)應(yīng)邊和對(duì)應(yīng)角下列全等三角形的對(duì)應(yīng)邊和對(duì)應(yīng)角1、 ABE A

6、CF對(duì)應(yīng)角是：對(duì)應(yīng)角是： A和和A、 ABE和和ACF、 AEB和和AFC；對(duì)應(yīng)邊；對(duì)應(yīng)邊是是AB和和AC、AE和和AF、BE和和CF。2、 BCE CBF對(duì)應(yīng)角是：對(duì)應(yīng)角是： BCE和和 CBF、 BEC和和CFB、 CBE和和 BCF。對(duì)應(yīng)邊是：。對(duì)應(yīng)邊是：CB和和BC、CE和和BF、CF和和BE。3、 BOF COE找一找找一找 平平 移移翻翻 折折旋旋 轉(zhuǎn)轉(zhuǎn)BAC.邊所在直線平移沿把BCABC.180邊所在直線翻折沿把BCABC.180旋轉(zhuǎn)繞點(diǎn)把BABCF圖8圖7圖6圖5EHGNMEDCBADFECBADCBA圖4圖3圖2圖1EDCBACBADEDCBAFEDCBA觀察:5.書(shū)寫(xiě)全等式

7、時(shí)要求把對(duì)應(yīng)字母放在對(duì)應(yīng) 的位置上2. 叫做全等三角形。 1.能夠重合的兩個(gè)圖形叫做 。全等圖形全等圖形4.全等三角形的 和 相等對(duì)應(yīng)邊對(duì)應(yīng)邊對(duì)應(yīng)角對(duì)應(yīng)角對(duì)應(yīng)頂點(diǎn)對(duì)應(yīng)頂點(diǎn)課課 堂堂 小小 結(jié)結(jié) 能夠重合的兩個(gè)三角形3.“全等”用符號(hào)“ ”來(lái)表示，讀作“ ”對(duì)應(yīng)邊對(duì)應(yīng)邊對(duì)應(yīng)角對(duì)應(yīng)角全等于全等于 其中：互相重合的頂點(diǎn)叫做 ;互相重合的邊叫做;互相重合的角叫做 .尋找對(duì)應(yīng)元素的規(guī)律尋找對(duì)應(yīng)元素的規(guī)律（1）有公共邊的，公共邊是對(duì)應(yīng)邊；）有公共邊的，公共邊是對(duì)應(yīng)邊；（2）有公共角的，公共角是對(duì)應(yīng)角；）有公共角的，公共角是對(duì)應(yīng)角；（3）有對(duì)頂角的，對(duì)頂角是對(duì)應(yīng)角；）有對(duì)頂角的，對(duì)頂角是對(duì)應(yīng)角；（4）兩個(gè)全等三角形最大的邊是對(duì)應(yīng)邊，）兩個(gè)全等三角形最大的邊是對(duì)應(yīng)邊， 最小的邊是對(duì)應(yīng)邊；最小的邊是對(duì)應(yīng)邊；（5）兩個(gè)全等三角形最大的角是對(duì)應(yīng)角，）兩個(gè)全等三角形最大的角是對(duì)應(yīng)角， 最小的角是對(duì)應(yīng)角；最小的角是對(duì)應(yīng)