How could they have written their definition of similarity with greater precision?
They couldn’t. Only problem is, they didn’t think about the result of precisely defining it that way.
Aha! So you’re saying the middle of page 141 is only talking about this example. You figure the book is saying in general, ABC[tilde]DEF does not imply A = D, B = E and C = F?
By specifying that the correspondence is necessary.
Which they didn’t do on the middle of page 141?
(If anyone’s not seeing the scans, you probably will if you accept cookies.)
No, this book earlier said it was customary (which I’d quibble with, but that’s a separate debate), so it is being consistent with its own statement.
It does not speak to generality, as it states only custom and not universality. I would take it to be true for any example in this book but not assume it is generally true, as the book itself says it is merely customary.
Quibble which way? It’s not customary, or it’s actually mandatory?
Clearly the former. The latter is not stated in the textbook, so it’s not there to quibble with.
Then the issue is with labelling vertices, which is always arbitrary. If you can rotate, scale and translate ABC to get it identical to DEF or any triangle, then it is similar. That’s what the textbook says. If you have a triangle EDF where angles A=E, B=D, C=F then it is still similar, it’s just another differently labelled but similar triangle, just like the text’s GHK. Also, a 3-4-5 triangle is similar to a 8-6-10 triangle.
If this confuses today’s students when reading the textbook - that’s why teachers are there, to (hopefully) clarify this for them.
I stopped scanning too soon. I’ve added page 142, where (Example 2A) the student is supposed to write that S is congruent to V and T is congruent to W. That’s what he’s supposed to conclude, given RST[tilde]UVW. Same on page 144 (Practice 1) – seeing GHJ[tilde]PQR, the student is expected to write G = P etc. In other words, students are instructed to assume the angles are in order. If triangle ABC is scalene, and ABC[tilde]DEF, then ABC[tilde] EFD is false.
In that example, students are explicitly told “Corresponding angles are listed in the same position in each triangle name.”
One might infer from this that students should not necessarily assume this unless they are explicitly told so.
In the Practice on page 144, students aren’t told anything. So the correct answer is “We don’t know”?
Depends on what you mean by “the correct answer”. The online automated homework system that comes with the textbook would probably assume that the vertices were listed in corresponding order, and so expect that for the “correct” answer, but if one of my students pointed out that it didn’t specify, I’d give them full credit.