“两条直线被一组平行线所截,所得的对应线段成比例”简称平行线分线段成比例定理,由此得出一个推论:平行于三角形一边的直线与其他两边相交,截得的对应线段成比例.例1如图1,在△ABC中,AD平分∠BAC交BC于点D.求证:AB /AC=BD /CD.分析从点C作AD的平行线或从点D作AC的平行线即可使用平行线分线段成比例定理,不妨选择前者作辅助线方法.证明如图1所示,从点C作CE∥AD交BA的延长线于点E,则 “The two straight lines are a set of parallel lines cut off, the resulting corresponding line segment proportional ” referred to as the parallel line sub-segment proportional theorem, which leads to a corollary: a line parallel to one side of the triangle intersection with the other two sides, cut Example 1 As shown in Figure 1, in Δ ABC, AD bisects ∠ BAC to BC at point D. Verify that AB / AC = BD / CD. Analyze the parallel line from point C to AD or from point D For parallel lines of AC parallel lines can be used to divide the line segment proportional theorem, may wish to select the former as the auxiliary line method.As shown in Figure 1, from point C for CE ∥ AD to BA extension line at point E, then