在几何学习中,求解或求证图形中的线段长度关系是一类常见的题目.下面介绍两种添加辅助线的方法,通过这些方法可以构造等腰三角形,从而求得线段长度间的关系.一以角平分线为对称轴构造等腰三角形例1如图1,在△ABC中,∠A=2∠B.CD平分∠ACB,AD=2.2,AC=3.6.求BC的长.分析:因为∠A=2∠B,AD=2.2,所以可以尝试转化∠A,以便出现一个等腰三角形.因为CD平分∠ACB,所以可在CB边上取一点E,使EC=AC,连接DE(如图2).这样, In geometry learning, it is a common problem to solve the relationship between the lengths of line segments in the graph or verify the graph. Two methods for adding auxiliary lines are introduced below. By these methods, the isosceles triangle can be constructed and the relationship between the lengths of line segments can be obtained. Constructed isosceles triangle with the angle bisector as the symmetry axis Example 1 In △ ABC, ∠A = 2∠B.CD bisect ∠ACB, AD = 2.2, AC = 3.6. ∠A = 2∠B, AD = 2.2, so try transposing ∠A so that an isosceles triangle appears. Because CD bisects ∠ACB, take a point E on the edge of CB to make EC = AC, connect DE Figure 2). In this way,