Updated 2013 June 15.
This is my appeal to my colleagues, and to the mathematical community, to stop using the acronym “CPCTC.” Here’s my case against CPCTC:
- Students cannot consistently recite the sentence that “CPCTC” abbreviates.
- The sentence itself sounds awkward and wordy: “The corresponding parts of congruent triangles are congruent.” Since the last three words are “triangles are congruent,” many students erroneously believe that the statement says that triangles are congruent. This is much the same error as saying that “the pockets of my jeans are dirty” is about dirty jeans, as opposed to dirty pockets.
- Students cite CPCTC at the wrong times. The classic error here is to assert that two triangles are congruent “by CPCTC.” This shows a lack of understanding on the part of the student.
- CPCTC tries to do two things at once: by means of the term “parts,” it tries to subsume statements about *angles* as well as *sides.”
The solution I propose is simple: instead of trying to do double-duty by using the term “parts,” let’s separate this idea into the following two statements:
- CT->CS: Congruent triangles have congruent sides. Or, if you prefer: “If two triangles are congruent, then they have congruent sides.”
- CT->CA: Congruent triangles have congruent angles.
Do you notice the same problems I mention above? What do you think of my proposed solution? Let me know what you think about this idea in the comments.