# Congruence

## Origin

The Latin *congruō* meaning “I meet together, I agree”.

## Definitions

- 1: the quality or state of agreeing, coinciding, or being congruent
- 2: a statement that two numbers or geometric figures are congruent

## Description

**Congruence** (≅) is the state achieved by coming together, the state of agreement. As an abstract term, congruence means similarity between objects. Congruence, as opposed to approximation, is a relation which implies a species of equivalence.

In geometry, two figures or objects are congruent if they have the same shape and size, or if one has the same shape and size as the mirror image of the other. More formally, two sets of points are called congruent if, and only if, one can be transformed into the other by an isometry, i.e., a combination of translations, rotations and reflections. This means that either object can be repositioned and reflected (but not resized) so as to coincide precisely with the other object. Two line segments are congruent if and only if they have the same length.

The related concept of similarity applies if the objects differ in size but not in shape.[1]