1.4全等三角形資料

1.4全等三角形1.觀察:以下各組圖形,它們能重合嗎?(1)(2)(3)(4)第1組第2組2.

能夠重合的兩個(gè)圖形叫做全等圖形.★★能夠重合的兩個(gè)三角形叫做全等三角形.3.全等三角形的表示方法

如圖△ABC和△DEF全等,記作△ABC≌△DEF.ABCDEF全等三角形的幾個(gè)有關(guān)概念DEFABC1.兩個(gè)全等三角形重合時(shí),能夠互相重合的頂點(diǎn)叫做全等三角形的對(duì)應(yīng)頂點(diǎn).互相重合的邊叫做全等三角形的對(duì)應(yīng)邊.互相重合的角叫做全等三角形的對(duì)應(yīng)角.注意表示兩個(gè)三角形全等時(shí),對(duì)應(yīng)點(diǎn)要寫在對(duì)應(yīng)的位置上.這樣容易找出對(duì)應(yīng)邊和對(duì)應(yīng)角.ABC“全等〞符號(hào)：≌如上圖：△ABC≌△DEF通常把對(duì)應(yīng)頂點(diǎn)的字母寫在對(duì)應(yīng)位置上DEF練習(xí)1.如圖:△AOB≌△COD.ABCDO(1)對(duì)應(yīng)點(diǎn)是:＿＿＿＿,＿＿＿＿,＿＿＿＿.(2)對(duì)應(yīng)邊是:＿＿＿＿,＿＿＿＿,＿＿＿＿.(3)對(duì)應(yīng)角是:＿＿＿＿,＿＿＿＿,＿＿＿＿.2.如圖△ABC≌△DCB.ABCD(1)對(duì)應(yīng)點(diǎn)是:＿＿＿＿＿＿＿＿＿＿.(2)對(duì)應(yīng)邊是:＿＿＿＿＿＿＿＿＿.(3)對(duì)應(yīng)角是:＿＿＿＿＿＿＿＿＿＿＿＿.點(diǎn)A和點(diǎn)C點(diǎn)O和點(diǎn)O點(diǎn)B和點(diǎn)DAB和CDAO和COBO和DO∠A和∠C∠B和∠D∠AOB∠COD點(diǎn)A和點(diǎn)D,點(diǎn)B和點(diǎn)C,點(diǎn)C和點(diǎn)BAB和DC,AC和DB,BC和CB∠A和∠D,∠ABC和∠DCB,∠ACB和∠DBC.叫做公共邊ABCDEF3.如圖△ABC≌△DEF.BC的對(duì)應(yīng)邊是＿＿;∠ACB的對(duì)應(yīng)角是＿＿＿.DF的對(duì)應(yīng)邊是＿＿.4.如圖△ABC≌△ADE.ABCDE∠ACB的對(duì)應(yīng)角是＿＿＿;∠A的對(duì)應(yīng)角是＿＿＿;AC的對(duì)應(yīng)邊是＿＿;DE的對(duì)應(yīng)邊是＿＿.EF∠DFEAC∠AED∠AAEBC叫做公共角5.如圖,△ABD≌△CDB.(1)對(duì)應(yīng)頂點(diǎn)是:＿＿＿＿,＿＿＿＿,＿＿＿＿＿;(2)對(duì)應(yīng)邊是:＿＿＿＿,＿＿＿＿,＿＿＿＿＿;(3)對(duì)應(yīng)角是:＿＿＿＿,＿＿＿＿＿＿＿,＿＿＿＿＿＿.ABCD點(diǎn)A和點(diǎn)C點(diǎn)B和點(diǎn)D點(diǎn)D和點(diǎn)BAB和CDAD和CBBD和DB∠A和∠C∠ABD=∠CDB∠ADB=∠CBD根據(jù)全等三角形的概念:能夠互相重合的三角形叫做全等三角形.所以得到:★★★全等三角形的性質(zhì)全等三角形的對(duì)應(yīng)邊相等,對(duì)應(yīng)角相等.問題ABCEF全等三角形的對(duì)應(yīng)邊相等1.如圖,△ACF≌△ABE,AB=6cm,AF=2cm.理由是＿＿＿＿＿＿＿＿＿＿＿＿＿.∠C=28°,則AC=＿＿cm,AE=＿＿cm,∠B=＿＿度.22862.如圖,△ABC≌△ADE,且∠BAC=30°,∠E=55°,那么∠EAD=＿＿＿,∠C=＿＿＿.ABCDE30°55°理由是＿＿＿＿＿＿＿＿＿＿＿＿.全等三角形的對(duì)應(yīng)角相等3.已知△ABC≌△DEF,A與D,B與E分別是對(duì)應(yīng)頂點(diǎn),∠A=50°,∠B=70°,BC=15cm,則∠F=＿＿,EF=＿＿cm.∠C=180°-50°-70°=60°ABCDEF60°154.如圖,△ACE≌△DBF,以下結(jié)論中正確的個(gè)數(shù)是()EACDFB12①AC=DB;②AB=DC;③∠1=∠2;④BC=AE;⑤5.如圖,△ABC≌△ADE,那么∠DAE=＿＿＿,ABCDE假設(shè)∠D=∠B,∠DAB=＿＿＿.√√√×√∠BAC∠EACA.2B.3C.4D.5C例二解：12ABCD圖1B(C)AD圖2∵AD平分∠BAC∴∠1=∠2因此將圖形(圖1)沿AD對(duì)折時(shí)，射線AC與射線AB重合圖1，AD平分∠BAC，AB=AC，

(1)△ABD與△ACD全等嗎？

(2)BD與CD相等嗎？∠B與∠C呢？請(qǐng)說明理由AB=AC∵點(diǎn)C與B重合，即△ABD與△ACD重合(圖2)∴△ABD≌△ACD∴BD=CD∴(全等三角形的對(duì)應(yīng)邊相等)∠B=∠C