发布网友 发布时间:2022-04-30 12:50
共1个回答
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