我们知道,等腰三角形两腰上的高相等,中线相等,两底角的平分线相等.其逆命题也成立.这就是对称性.如线段中垂线定理,角平分线定理,平行线及圆的相关定理也都是可逆的.这也是反身性.但是,由于角平分线与高线和中线相比条件明显弱化(没有垂足,中点的具体直观性及其与边的直接联系),导致了Steiner-Lehmes定理证明的难度.但因此也引起数学爱好者的广泛关注,人们潜心于该定理不同证法的探究及形式多样的引申,几十年来趋之若鹜.其中,尤以比例性质、相似、圆幂定理、正弦定理、角平分线定理、面积法(共边定理,共角定理)和繁琐的代数证法 We know that the isosceles triangle is equally high on both sides of the waist, and the center lines are equal and the bisector of the bottom corners are equal. The inverse conjecture is also established. This is symmetry, such as the vertical line theorem, the angle bisector theorem, the parallel lines and The relevant theorems for the circle are also invertible, which is also reflexive. However, since the condition of the angle bisector is significantly weaker than that of the high line and the middle line (there is no specific visualization of the foot-drop, the midpoint and its direct relation to the side) , Which led to the difficulty of Steiner-Lehmes theorem proving, but it also aroused widespread concern of math enthusiasts, people devoted themselves to the theorem of different syndromes of inquiry and various forms of extended, decades flock, including, in particular, the proportion of nature, Similar, circular power theorem, sine theorem, angle bisector theorem, area method (co-edge theorem, co-argument theorem) and cumbersome algebraic card method