# What is CPCTC: Property, definition..?

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?

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

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I would imagination the definition category, but you should be able to check this by looking at the definition you have been given for "congruent". –  Gerry Myerson Oct 11 '12 at 3:28
There are a lot of equivalence relations around. Congruence is not just an equivalence relation --- it is a very specific equivalence relation, and unless you know what congruence means, you can't even ask your question, much less answer it. –  Gerry Myerson Oct 11 '12 at 6:04

## 1 Answer

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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I know what CPCTC is and how to use it, I am wondering if it is a theorem, definition, or the like. –  SomekidwithHTML Oct 11 '12 at 7:01
@SomeidithHTML Yes and I mentioned above that it is a theorem whose proof follows directly from the definition of congruence given. –  Jeremy Oct 11 '12 at 19:14
haha, sorry i don't seem to be able to read. Thanks. –  SomekidwithHTML Oct 12 '12 at 0:05