两三角形的垂三角形有向面积的定值定理及应用

On Some Fixed Value Theorems for Directed Area of Two Triangles’Orthologic Triangles and Their Applications

摘要: 利用有向面积定值法研究两个三角形的透视性.通过介绍两三角形的垂三角形的有关概念, 给出了两三角形及其垂三角形有向面积的一个关系定理, 并据此得到两三角形的顶点向量数量积的定值定理, 以及两三角形垂直透视的几个充分必要条件.结论表明, 这些充分必要条件都和两三角形的坐标的某种对称性有关.

Abstract: In this paper, the orthogonality of two triangles is investigated by fixed value methods of directed areas.The concepts of orthologic triangle are intruduced first, and then a theorem for directed areas of two triangles and their orthologic triangles is obtained, thus a fixed value theorem for vertices' vectors of the two triangles is obtained and some necessary and sufficient conditions for orthogonality of the two triangles are proved.Results show that these necessary and sufficient conditions are related with some symmetry of the vertices of the two triangles.