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

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.