Congruence (geometry) size. (Most definitions consider congruence to be a form of similarity, although a minority require that the objects have different sizes in order to qualify as similar.) For two polygons to be congruent, they must have an equal number of sides (and hence an equal number—the same number—of vertices). Two polygons with "n" sides are congruent if and only if they each have numerically identical sequences (even if clockwise for one polygon and counterclockwise for the other) side-angle-side-angle-... for "n" sides and "n" angles. Congruence of polygons can be established graphically as follows: If at any time the step cannot
Coxeter decompositions of hyperbolic polygons Coxeter decompositions of hyperbolic polygons A Coxeter decomposition of a polygon is a decomposition into a finite number of polygons in which any two sharing a side are reflections of each other along that side. Hyperbolic polygons are the analogues of Euclidean polygons in hyperbolic geometry. A hyperbolic "n"-gon is an area bounded by "n" segments, rays, or entire straight lines. The standard model for this geometry is the Poincaré disk model. A major difference between Euclidean and hyperbolic polygons is that the sum of internal angles of a hyperbolic polygon is not the same as Euclidean polygons. In particular,