《判定三角形全等与相似的一种新方法及其证明》一文的有关注记 (Ⅱ)

Annotations(II) on A New Criterion for Triangle Congruence and Similarity with Proof

摘要

文中采用几何和代数相结合的方法,并利用反证法,解决了文献[1]定理补充说明第三点中提及的待解答的问题.首先,假设已知相等的两条角平分线所平分的角不等,然后根据文献[1]中的引理四,得出两个三角形中,除一对对应边已知相等外的另两对对应边的大小关系.之后,在此基础上,通过角平分线长和中线长的计算公式得出矛盾,从而证明三角形全等.

Abstract

This paper settled the open question posed in the third item of the supplementary statement to the theorem in Reference [1] by integrating geometric and algebraic techniques and employing proof by contradiction. First, assuming that the angles bisected by two equal—length angle bisectors are unequal. Then based on Lemma 4 in Reference [1], the relationships between the lengths of the other two pairs of corresponding sides (besides the already known equal pair) of the two triangles are obtained. Building on this, by applying the formulas for the lengths of angle bisectors and medians, a contradiction is derived, thereby proving the triangles congruent.

关键词

三角形 / 边 / 角平分线 / 中线 / 全等

Key words

riangle / side / anglebisector / median / congruence

参考文献

[1] 米其韬. 判定三角形全等与相似的一种新方法及其证明[J/OL].[2025—04—03]. https://lib.cqvip.com/Qi—kan/Article/ReadIndex?id=7002790733&info=fkk71bZ8WUcSJYZS%2b4htipzZbyO%2bgKerN5AQnOfS26lCR3se%2ffgs%2bQ%3d%3d.