Question

如圖所示，沿直線AC對(duì)折，△ABC與△ADC重合，則△ABC≌________，AB的對(duì)應(yīng)邊是________，BC的對(duì)應(yīng)邊是________，∠BCA的對(duì)應(yīng)角是________．

Answer 1

△ADC    AD    AC    ∠DCA
分析：兩個(gè)三角形的形狀、大小、都一樣時(shí)，其中一個(gè)可以經(jīng)過平移、旋轉(zhuǎn)、翻折等運(yùn)動(dòng)（或稱變換）使之與另一個(gè)完全重合，則這兩個(gè)三角形是全等三角形．再由對(duì)應(yīng)點(diǎn)確定對(duì)應(yīng)邊和對(duì)應(yīng)角即可．
解答：沿直線AC對(duì)折，△ABC與△ADC重合，則△ABC≌△ADC，AB的對(duì)應(yīng)邊是 AD，BC的對(duì)應(yīng)邊是 AC，∠BCA的對(duì)應(yīng)角是∠DCA．
點(diǎn)評(píng)：此題考查全等三角形的定義和確定全等三角形的對(duì)應(yīng)邊、對(duì)應(yīng)角的方法：
一、根據(jù)對(duì)應(yīng)頂點(diǎn)來找對(duì)應(yīng)邊和對(duì)應(yīng)角．如果已知兩個(gè)三角形的頂點(diǎn)是對(duì)應(yīng)點(diǎn)，則以對(duì)應(yīng)點(diǎn)為頂點(diǎn)的角是對(duì)應(yīng)角，對(duì)應(yīng)角的對(duì)邊就是對(duì)應(yīng)邊；
二、對(duì)應(yīng)角和對(duì)應(yīng)邊確定法；
已知兩個(gè)全等三角形的一組對(duì)應(yīng)角和一組對(duì)應(yīng)邊已知，則可根據(jù)對(duì)應(yīng)邊的對(duì)角是對(duì)應(yīng)角，對(duì)應(yīng)角的對(duì)邊是對(duì)應(yīng)邊來確定對(duì)應(yīng)元素．