Triangles of same shape and size are congruent.

Corresponding parts of congruent triangles are congruent. (CPCTC)

Each triangle has six parts, six angles and six sides. If all the corresponding parts of two triangles are congruent, then the two triangles are congruent.

If Δ ABC is congruent to Δ DEF, the vertices of the two triangles correspond in the same order as the letters used to denote them.

Congruence of triangles are reflexive, symmetric and transitive.

Δ

_{1} ≅ Δ

_{1} Reflexive

If Δ

_{1} ≅ Δ

_{2}, the Δ

_{2} ≅ Δ

_{1} Symmetric

If Δ

_{1} ≅ Δ

_{2} and Δ

_{2} ≅ Δ

_{3}, then Δ

_{1} ≅ Δ

_{3} Transitive

**The congruence postulates or theorems are used to prove congruence are given below:**1.

Side - Side - Side Congruence (SSS)

Two triangles are congruent, if the three sides of a triangle are congruent respectively to the corresponding sides of the other triangle.

2.

Side - Angle - Side Congruence (SAS)

Two triangles are congruent if two sides and included angle of one of the triangle are respectively congruent to the two sides and included angle of the other triangle.

3.

Angle - Side - Angle congruence (ASA)

Two triangles are congruent if two angles and the included side of one triangle are respectively congruent to two angles and the included side of the other triangle.

4.

Angle - Angle - Side congruent (AAS)

Two triangles are congruent if two angles and a non included side of a triangle are respectively congruent to two angles and a non included side of the other triangle.

Proving triangle congruence and using CPCTC consequently are widely used in solving many geometrical problems.

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