Define congruence in terms of rigid motions, identify corresponding parts from a congruence statement, and apply CPCTC correctly.
Two figures are defined to be congruent exactly when a sequence of rigid motions maps one exactly onto the other -- congruence is not a separate new idea, it is what "the same rigid-motion journey" produces. When two triangles are congruent, we write triangle ABC ~= triangle DEF, and the ORDER of the letters is not decoration: it lines up corresponding vertices, so A matches D, B matches E, and C matches F. From that single statement, every corresponding pair of sides and angles is automatically congruent too, because rigid motions preserve both distance and angle measure.
This gives us CPCTC -- Corresponding Parts of Congruent Triangles are Congruent -- one of the most useful reasons in geometry proof-writing. CPCTC is not a way to prove two triangles congruent; it is what you are allowed to conclude AFTER two triangles have already been proven congruent by some other method. A typical proof plan has two stages: first prove the triangles congruent, then use CPCTC to reach a fact that was not obvious on its own.
Mastery looks like: They correctly identify corresponding parts from a congruence statement using letter order, and apply CPCTC only after triangle congruence has already been established.
Common stumbles: Matching corresponding parts by position in a drawing instead of by letter order in the congruence statement; using CPCTC as the reason for the very step that is supposed to prove congruence.