若三角形一边上的一点和这边所对的顶点将三角形的周长二等分,人们则称这一点为三角形的周界中点,并将以三个周界中点为顶点的三角形称为周界中点三角形. 本文在文[1]、[2]的基础上,进一步研究周界中点三角形并得到了两个有趣的性质. 引理 设D、E、F分别是△ABC的边BC、CA、AB上的周界中点,且BC=a,CA=b,AB=c,s=1/2(a+b+c),则 AE=BD If a point on one side of the triangle and a vertex on the side bisect the perimeter of the triangle, one would call this the midpoint of the perimeter of the triangle, and the triangle with the midpoint of the three perimeters as the vertex would be called the perimeter midpoint triangle. On the basis of [1] and [2], this paper further studies the midpoint triangle of the perimeter and obtains two interesting properties. Lemma designates that D, E, and F are the perimeters of the edges BC, CA, and AB of △ABC, respectively. Point, and BC = a, CA = b, AB = c, s = 1/2 (a + b + c), then AE = BD