Definition of Congruence of Triangles:
Congruence of triangles refers to the condition when two triangles have the same size and shape. In other words, if two triangles are congruent, their corresponding sides and angles are equal.

Criteria for Congruence of Triangles:
For two triangles to be congruent, they must satisfy one of the following criteria:
1. Side-Side-Side (SSS) Criterion: All three sides of one triangle are equal to the corresponding sides of the other triangle.
2. Side-Angle-Side (SAS) Criterion: Two sides and the included angle of one triangle are equal to the corresponding sides and angle of the other triangle.
3. Angle-Side-Angle (ASA) Criterion: Two angles and the included side of one triangle are equal to the corresponding angles and side of the other triangle.
4. Angle-Angle-Side (AAS) Criterion: Two angles and a non-included side of one triangle are equal to the corresponding angles and side of the other triangle.

Importance of Congruence of Triangles:
Understanding congruence of triangles is essential in geometry as it helps in proving various properties and theorems. It allows us to establish relationships between different parts of triangles and solve problems involving triangles.

Examples of Congruence of Triangles:
1. If two triangles have sides of lengths 3 cm, 4 cm, and 5 cm, they are congruent by the SSS criterion.
2. If two triangles have angles of measures 30°, 60°, and 90°, they are congruent by the ASA criterion.

In conclusion, congruence of triangles is a fundamental concept in geometry that helps in proving the equality of triangles based on their corresponding sides and angles. By understanding the criteria for congruence, one can apply this concept to solve various geometric problems effectively.