全等三角形的定義及性質(zhì)

全等三角形----------定義及性質(zhì)三角形三邊關(guān)系12345三線的定義三角形內(nèi)角和三角形外角定理多邊形內(nèi)角和與外角和回顧一個(gè)圖形經(jīng)過平移,翻折,旋轉(zhuǎn)后,位置變化了,但＿＿＿和＿＿＿都沒有改變,即平移,翻折,旋轉(zhuǎn)前后的圖形______。能夠完全重合的兩個(gè)圖形叫做全等形我們發(fā)現(xiàn)形狀大小完全重合觀察：在上面的圖形中哪些是全等形？①②③④⑤⑥⑦⑧⑨⑩1211牢記：如果兩個(gè)圖形全等，它們的形狀和大小一定都相同！全等三角形能夠完全重合的兩個(gè)三角形,叫做全等三角形ABCEDF如圖△ABC與△DEF全等用符號(hào)“≌”表示記作：△ABC≌△DEF讀作：“△ABC全等于△DEF”互相重合的頂點(diǎn)叫對(duì)應(yīng)頂點(diǎn).互相重合的邊叫對(duì)應(yīng)邊.互相重合的角叫對(duì)應(yīng)角.注意：書寫全等式時(shí)要求把對(duì)應(yīng)頂點(diǎn)字母放在對(duì)應(yīng)的位置上。全等三角形的性質(zhì)全等三角形的對(duì)應(yīng)邊相等，全等三角形的對(duì)應(yīng)角相等。ABCDEF已知△ABC≌△DEF，則有：AB=DE，BC=EF，AC=DF；（全等三角形對(duì)應(yīng)邊相等）∠A=∠D，∠B=∠E，∠C=∠F（全等三角形對(duì)應(yīng)角相等）小測(cè)試1.如圖△ABC≌△ADE若∠D=∠B，∠C=∠AED，則AD=

?！螪AE=

；ABCDEABCDE∠BAC

ＡＢ找對(duì)應(yīng)邊和對(duì)應(yīng)角⑴.平移⑵.翻折⑶.旋轉(zhuǎn)三角形的全等變換ABCDEF先寫出全等式，再指出它們的對(duì)應(yīng)邊和對(duì)應(yīng)角試一試(1)：∵△ABC≌△DEF∴AB=DE,BC=EF,AC=DF.∴∠A=∠D,∠B=∠E,∠C=∠F.平移ABCD先寫出全等式，再指出它們的對(duì)應(yīng)邊和對(duì)應(yīng)角試一試(2)：∵△ABC≌△ABD∴AB=AB,

BC=BD,

AC=AD.∴∠BAC=∠BAD,

∠ABC=∠ABD∠C=∠D.規(guī)律一：有公共邊的，公共邊是對(duì)應(yīng)邊翻折先寫出全等式，再指出它們的對(duì)應(yīng)邊和對(duì)應(yīng)角試一試(3)：ACODB∵△AOC≌△BOD∴AO=BO,

AC=BD,

OC=OD.∴∠A=∠B,

∠C=∠D,∠AOC=∠BOD.規(guī)律二：有對(duì)頂角的，對(duì)頂角是對(duì)應(yīng)角旋轉(zhuǎn)ABCDE先寫出全等式，再指出它們的對(duì)應(yīng)邊和對(duì)應(yīng)角試一試(4)：∵△ABC≌△ADE∴AB=AD,

AC=AE,

BC=DE∴∠A=∠A,

∠B=∠D,∠ACB=∠AED.規(guī)律三：有公共角的，公共角是對(duì)應(yīng)角規(guī)律四：一對(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ABCDE先寫出全等式，再指出它們的對(duì)應(yīng)邊和對(duì)應(yīng)角試一試(5)：∵△ABC≌△DEC∴AB=DE,

AC=DC,

BC=EC∴∠A=∠D,∠B=∠E,∠ACB=∠DCE.BC

AFDE先寫出全等式，再指出它們的對(duì)應(yīng)邊和對(duì)應(yīng)角試一試(6)：∵△ABC≌△FDE∴AB=FD,

AC=FE,BC=DE∴∠A=∠F,∠B=∠D,∠ACB=∠FED.規(guī)律四：一對(duì)最大的角時(shí)對(duì)應(yīng)角一對(duì)最小的角是對(duì)應(yīng)角例：如圖△ABD≌△EBC，AB=3cm,BC=5cm,求DE的長(zhǎng)學(xué)以致用解：∵△ABD≌△EBC∴EB=AB=3cm

BD=BC=5cm∴DE=BD-EB=5-3=2cmP82.（江蘇南通中考題）如圖，△OAD≌△OBC，且∠O=70°，∠D=∠C=25°下列結(jié)論①OD=OC，②BC=OD，③BD=AC正確的有

。

A.1個(gè)B.2個(gè)C.3個(gè)D.4個(gè)3、如圖，△ABC與△DEF全等，∠F=∠C，∠D=∠A，AD=12cm，BE=2cm，求線段AB的長(zhǎng)________。

【典例精講】P11（課堂檢測(cè)）10、已知△ABC≌△A'B'C',∠A=∠A',∠B=∠B'，∠C=70°，AB=15cm,則∠C'=______，A'B'=_______。11、如圖，距形ABCD沿DE折疊，點(diǎn)C恰好落在BA邊上，得點(diǎn)C',使∠C'EB=40°，求∠EDC'的度數(shù)限時(shí)練習(xí)1.已知△DEF≌△MNP，且EF=NP，∠F=∠P，∠D=48°，∠E=52°。MN=12，求∠P的度數(shù)及DE的長(zhǎng)2.將△ABC沿直線BC平移到△ECD（1）相等的邊有

，相等的對(duì)應(yīng)角有

。（2）∠ACE=∠E嗎？為什么？ABCDE3.如圖所示，四邊形ABCD是梯形，AD∥BC，若DE∥AC交BC的延長(zhǎng)線與點(diǎn)E，且△ADC≌△ECD，梯形ABCD的面積和△BDE的面積相等嗎？4.如圖，將周長(zhǎng)為8的△ABC沿BC方向平移一個(gè)單位得到△DEF，則四邊形ABFD的周長(zhǎng)為（）A.6B.8C.10D.12ADBCEABCDEF目標(biāo)完成寶貝們棒棒噠?(°?‵?′??)DiagramTEXT1isaDesignDigitalContent&Contents2isaDesignDigitalContent&Contents4isaDesignDigitalContent&Contents3isaDesignDigitalContent&Contents5isaDesignDigitalContent&ContentsCycleTEXT12345DiagramTitleThemeGalleryisaDesignDigitalContent&ContentsmalldevelopedbyGuildDesignInc.TitleThemeGalleryisaDesignDigitalContent&ContentsmalldevelopedbyGuildDesignInc.DiagramClicktoaddTitleClicktoaddTitleClicktoaddTitleClicktoaddTitleDiagramtextThemeGalleryisaDesignDigitalContent&ContentsmalldevelopedbyGuildDesignInc.textThemeGalleryisaDesignDigitalContent&ContentsmalldevelopedbyGuildDesignInc.textThemeGalleryisaDesignDigitalContent&ContentsmalldevelopedbyGuildDesignInc.DiagramThemeGalleryisaDesignDigitalContent&ContentsmalldevelopedbyGuildDesignInc.ThemeGalleryisaDesignDigitalContent&ContentsmalldevelopedbyGuildDesignInc.ThemeGalleryisaDesignDigitalContent&ContentsmalldevelopedbyGuildDesignInc.ThemeGalleryisaDesignDigitalContent&ContentsmalldevelopedbyGuildDesignInc.ThemeGalleryisaDesignDigitalContent&ContentsmalldevelopedbyGuildDesignInc.T

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