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So we're doing proofs in class and I was wondering:

Normally in two-column proofs you need Statements and Reasons, where Reasons are normally postulates, definitions, other theorems, or givens.

What category does CPCTC (Corresponding Parts of Congruent Triangles are Congruent) fit into? If it is a theorem, is there a proof for it?

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Congruent has been defined as an equivalence relation; a relation that fulfills Reflexivity, Symmetry, and Transitivity.

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1 Answer

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It is a theorem that immediately follows from the definition of congruence (depending on what definition you're using), From Wikipedia:

"Two triangles are congruent if their corresponding sides are equal in length and their corresponding angles are equal in size."

So if sides and angles of a triangle are equal they are clearly congruent. Also see this

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