My Geometry class is doing triangle congruency proofs these days. In general, we find three pairs of congruent parts (sides or angles) in two triangles; we show that these congruencies reveal that the triangles are either congruent or similar; and we conclude that further parts are congruent (in the case of congruent triangles) or proportional (in the case of similar triangles).
In the column of justifications, therefore, the last two justifications are usually SSS (or SAS or ASA or AAS or AAA) and then either CPCTC (Corresponding Parts of Congruent Triangles are Congruent) or Definition of Similarity.
I’ve done pretty much the same thing each time I’ve taught Geometry, but this year we’re using a text by Pearson in which this topic appears in Chapter 4. After doing this a zillion times, I have begun to wonder something about this nomenclature.
Why is that where triangles are CONGRUENT, we DO refer to CPCTC, and we DO NOT refer to a definition; but where triangles are SIMILAR, we DO NOT refer to CSSTP, but we DO refer to a definition?