Similarity (geometry) objects similar if one appears congruent to the other when zoomed in or out at some level. For example, all circles are similar to each other, all squares are similar to each other, and all equilateral triangles are similar to each other. On the other hand, ellipses are not all similar to each other, rectangles are not all similar to each other, and isosceles triangles are not all similar to each other. If two angles of a triangle have measures equal to the measures of two angles of another triangle, then the triangles are similar. Corresponding sides of similar polygons
Coxeter decompositions of hyperbolic polygons of polygons in which any two sharing a side are reflections of each other along that side. The goal of a Coxeter decomposition is to break up a polygon into a composition of congruent triangles reflected on its sides. If triangle ABC can undergo Coxeter decomposition and has angles formula_1, where formula_2 is the number of times the formula_3th angle is broken up, the triangle ABC can be written as formula_4. Several properties of these fundamental polygons are known for hyperbolic triangles. Quadrilaterals may also have Coxeter decompositions. Coxeter decompositions of hyperbolic polygons A Coxeter decomposition of a polygon is