Congruence

Definition:

Congruence is a mathematical relation between two objects that implies similarity, equivalence, or equality of their corresponding characteristics.

Types of Congruence

1. Geometric Congruence:

Geometric congruence refers to the equality of shapes and sizes of geometric objects such as line segments, angles, triangles, or polygons.

2. Number Congruence:

Number congruence refers to a relationship between two numbers, where they have the same remainder when divided by a specific whole number called the modulus.

3. Algebraic Congruence:

Algebraic congruence refers to the equality of algebraic expressions or equations, taking into account the rules and properties of algebraic operations.

Properties of Congruence

1. Reflexive Property:

If object A is congruent to object A, then the congruence relation is reflexive.

2. Symmetric Property:

If object A is congruent to object B, then object B is also congruent to object A, resulting in a symmetric congruence relation.

3. Transitive Property:

If object A is congruent to object B, and object B is congruent to object C, then object A is congruent to object C, illustrating the transitive nature of congruence.

4. Addition Property of Congruence (APC):

If object A is congruent to object B, and object C is congruent to object D, then the sum of A and C is congruent to the sum of B and D, according to the addition property of congruence.