角平分线对应边的比例
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发布时间：2022-04-30 12:50
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热心网友
时间：2022-06-22 08:12
(1) 过C作CE∥DA，交BA的延长线于E．∵CE∥DA∴∠1＝∠E，∠2＝∠3，∠1＝∠2∴∠E＝∠3∴AE＝AC∵CE∥DA∴BD/DC＝BA/AE又∵AE＝AC∴BD/DC＝AB/AC
(2)在BA延长线上取点C'，使AC'=AC，过C'作C'D'//CD交DA延长线于点D',连接C'D.∵C'D'//CD，A是BA与DD'的交点∴△ABD∽△AC'D'∴BD/C'D'=AB/AC'∵C'D'//CD∴∠C'D'A=∠ADB∵AD是三角形ABC外角的平分线∴∠C'AD=∠CAD∵AC'=AC,AD是公共边∴△C'AD≌△CAD∴∠C'DA=∠ADB,C'D=CD∴∠C'DA=∠C'D'A∴C'D'=C'D=CD∴BD/DC=BD/C'D'=AB/AC'=AB/AC