Triangle Congruence Postulates are foundational principles in geometry that determine when two triangles are congruent, meaning they have the same size and shape. The main postulates include Side-Side-Side (SSS), Side-Angle-Side (SAS), Angle-Side-Angle (ASA), Angle-Angle-Side (AAS), and Hypotenuse-Leg (HL) for right triangles, each providing specific conditions under which congruence can be established.