等腰三角形是一种特殊的三角形,它的性质和判定在计算和证明中有着广泛的应用.当图形中无明显的等腰三角形时,可根据条件和图形的特征,适当添加辅助线,如延长线段、作平行线,构造等腰三角形,利用等腰三角形的性质解决问题.一、延长线段法直接构造等腰三角形例1如图1,在△ABC中,AD平分∠BAC,∠B=2∠C.求证:AB+BD=AC. Isosceles triangle is a kind of special triangle, its nature and judgment has a wide range of applications in calculation and verification.When there is no obvious isosceles triangle in the graph, according to the characteristics of the conditions and graphics, add the appropriate auxiliary line, such as Extension of the line segment, as a parallel line, the construction of isosceles triangle, the use of isosceles triangle to solve the problem. First, the extension of line method directly construct isosceles triangle Example 1 In △ ABC, AD bisect ∠ BAC, ∠ B = 2∠C. Proof: AB + BD = AC.