Triangles | Incidence geometry | Geometry | Configurations (geometry)
Similarity system of triangles
A similarity system of triangles is a specific configuration involving a set of triangles. A set of triangles is considered a configuration when all of the triangles share a minimum of one incidence relation with one of the other triangles present in the set. An incidence relation between triangles refers to when two triangles share a point. For example, the two triangles to the right, and , are a configuration made up of two incident relations, since points and are shared. The triangles that make up configurations are known as component triangles. Triangles must not only be a part of a configuration set to be in a similarity system, but must also be directly similar. Direct similarity implies that all angles are equal between two given triangle and that they share the same rotational sense. As is seen in the adjacent images, in the directly similar triangles, the rotation of onto and onto occurs in the same direction. In the opposite similar triangles, the rotation of onto and onto occurs in the opposite direction. In sum, a configuration is a similarity system when all triangles in the set, lie in the same plane and the following holds true: if there are n triangles in the set and n − 1 triangles are directly similar, then n triangles are directly similar. (Wikipedia).
