Incenter centers known to the ancient Greeks, and the only one that does not in general lie on the Euler line. It is the first listed center, X(1), in Clark Kimberling's Encyclopedia of Triangle Centers, and the identity element of the multiplicative group of triangle centers. For polygons with more than three sides, the incenter only exists for tangential polygons—those that have an incircle that is tangent to each side of the polygon. In this case the incenter is the center of this circle and is equally distant from all sides. It is a theorem in Euclidean geometry that the three
Corresponding sides and corresponding angles example if in a polygon with the side sequence "abcde" and another with the corresponding side sequence "vwxyz" we have vertex angle "A" appearing between sides "a" and "b" then its corresponding vertex angle "V" must appear between sides "v" and "w". Corresponding sides and corresponding angles In geometry, the tests for congruence and similarity involve comparing corresponding sides and corresponding angles of polygons. In these tests, each side and each angle in one polygon is paired with a side or angle in the second polygon, taking care to preserve the order of adjacency. For example, if one polygon has