(related to Definition: Equivalence Relation)
It is easy to verify the reflexivity, symmetry and transitivity of the following properties. Thus, all these properties are equivalence relations. 1. Equality of numbers 1. Parallelity of straight lines in the plane 1. Sets having the same cardinality. 1. Similarity of shapes in the plane. Two shapes in a plane are said to be similar if one can be transformed into another by a combination of enlargements, reflections, translations or rotations. The similarity of shapes is an equivalence class. The following figure shows two similar shapes.