Given the congruent triangles below, is the statement “Triangle *ABC* can be proved congruent to triangle *ZYX*” true, or false?

I imagine most will say that the statement is false, and argue that the correspondence of the triangles is incorrect. That is, segment *AB* is not congruent to segment *ZY*, and so on. I think this is a reasonable response.

However, a substantial part of me believes the statement is true. “Triangle *ABC*” references an object, as does “triangle *ZYX*“. These two objects are indeed congruent. Thus, how can it be said they can’t be proved congruent?

In other words, I don’t believe the statement “Triangle *ABC* can be proved congruent to triangle *ZYX” *entails a binding correspondence in the way that the statement

does.

I was thinking about this because of this question from the June 2016 Common Core Geometry Regents exam.

According to the rubric, the correct answer is (3) *reflection over the x-axis*. The most common incorrect response, of course, was (1) *rotation. *But I’m not certain it’s really incorrect. I don’t think anyone would get this question wrong based on my objection, but since the question is designed to entice students to say *rotation*, I think it deserves some scrutiny.

**Related Posts**

- Regents Recaps
- Regents Recap — August 2015: Trouble with Transformations
- Regents Recap — January 2015: Questions with No Correct Answer