




Figure 1 Congruent triangles.


Corresponding parts
The parts of the two triangles that have the same measurements (congruent) are referred to as corresponding parts. This means that Corresponding Parts of Congruent Triangles are Congruent (CPCTC). Congruent triangles are named by listing their vertices in corresponding orders. In Figure 1 , Δ BAT ≅ Δ ICE.
Example 1: If Δ PQR ≅ Δ STU which parts must have equal measurements?




These parts are equal because corresponding parts of congruent triangles are congruent. Tests for congruence
To show that two triangles are congruent, it is not necessary to show that all six pairs of corresponding parts are equal. The following postulates and theorems are the most common methods for proving that triangles are congruent (or equal). Postulate 13 (SSS Postulate): If each side of one triangle is congruent to the corresponding side of another triangle, then the triangles are congruent (Figure 2 ).


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