CPCTC
/ C-P-C-T-C /
CPCTC is the workhorse phrase 'corresponding parts of congruent triangles are congruent'. It is the payoff step: once you have shown two triangles congruent (by SSS, SAS, ASA, AAS, or HL), you may then conclude that any pair of matching sides or matching angles is equal. The congruence is established with three facts; CPCTC harvests all the rest.
Precisely: if triangle ABC is congruent to triangle DEF, then because the correspondence A-D, B-E, C-F is built into the congruence, every corresponding pair agrees — angle A = angle D, angle B = angle E, angle C = angle F, |AB| = |DE|, |BC| = |EF|, |CA| = |FD|. In a two-column proof, the chain is: gather three congruence facts, cite the matching criterion to assert the triangles are congruent, then cite CPCTC to extract the one particular side or angle equality you actually wanted. It is the bridge from 'the triangles match' to 'this segment equals that segment'.
The order is non-negotiable: you may invoke CPCTC only after a congruence is proven, never before. Using CPCTC to justify the very equality you needed to establish the congruence is circular. And the correspondence must be the proven one — match parts by the letter order of the congruence statement, not by appearance in the diagram.
To show two segments AB and DE are equal, you first prove triangle ABC congruent to triangle DEF (say by SAS). Then by CPCTC, the corresponding sides AB and DE are equal — the conclusion you were after.
Prove congruence first, then CPCTC delivers every matching part.
CPCTC may be used only after congruence has been established, and only for parts that truly correspond. Using it to prove the congruence itself is circular reasoning.