How can we prove that triangles are congruent?

Two Triangles- are congruent if and only if all their corresponding sides and angles are congruent.

Side-Side-Side Triangle Postulate (SSS)- If 3 sides of a triangle are congruent to 3 sides of another triangle then the two triangles are congruent. 
Triangles ABC=XYZ

Side-Angle-Side Triangle Postulate (SAS)- If 2 sides of a triangle and the included angle are congruent to the 2 sides of another triangle and its included angle , 
then the two triangles are congruent.Triangles ABC=XYZ

Angle-Side-Angle (ASA)- triangles are congruent if any two angles and their included side are equal in both triangles.
Triangles ABC=XYZ


Angle-Angle-Side congruence Postulate (AAS)- Triangles are congruent if two pairs of corresponding angles and a pair of opposite sides are equal in both triangle.
Triangle ABC=XYZ