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《中小学数学》(初中版)2009年第12期刊载的“不一定全等吗?”一文(下称文[1]),证明了有关三角形全等的一个有趣命题,即“有两边及其中一边对角的平分线对应相等的两个三角形全等.”阅后受益匪浅,本文将另辟蹊径,从相似的角度作进一步探究.联想到相似三角形的性质,文[1]命题的一个类似便油然而生,即“有两边及其中一边对角的平分线对应成比例的两个三角形相似.”这一命题是否正确呢?回答是肯定的.下面将给出其探析思路,供读者参考.命题1在△ABC与△A_1B_1C_1中,AD、A_1D_1分别为么BAC、B_1A_1C_1的平分线,若AB/A_1B_1=BC/B_1C_1=AD/A_1D_1,则△ABC～△A_1B_1C_1.
The article “Is not necessarily congruent?” (No. [1]) in “Mathematics of Primary and Secondary Schools” (Junior High School Edition), 2009, No. 12, proves an interesting proposition about equality of triangles, that is, There are two sides and one side of the diagonal bisector equal to the equivalent of two triangles congruent. “After reading benefit, this article will find another way, from a similar point of view for further exploration.Remember the nature of similar triangles, [1] A similar analogy of the proposition arises spontaneously, that ”the bisector on both sides and one of the diagonals corresponds to a proportional two triangles." Is the proposition correct? The answer is affirmative Proposition 1 In △ ABC and △ A_1B_1C_1, AD, A_1D_1 are the bisectors of BAC and B_1A_1C_1 respectively, and △ ABC ~ △ A_1B_1C_1 if AB / A_1B_1 = BC / B_1C_1 = AD / A_1D_1.