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I am trying to say

Construct $\triangle ABC$ such that the extension of side CB is adjacent to side AB

I am trying to avoid using poor ambiguous vocabularies like "to the right of AB"

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Re-posted answer + comments, per OP's request:


You'll might want to specify that $A, \;B$ and $C$ are three non-colinear points (hence form a triangle), otherwise if A, B and C all lie on a line, then "adjacent" might be ambiguous. Consider, for example,:

Crudely, e.g.,

A________B________C

Then to specify the order in which the points are arranged, add your adjacency stipulation.

Note: While asserting the existence of three non-colinear points asserts the existence of a triangle, some might argue that the converse is not necessarily true. (That is, some might argue that a straight line is a degenerate triangle, but that's probably beyond the scope of your task.)

However, you can justifiably assume that, by definition:

$|AB| + |BC| > |AC| \iff A, B, C \text{ are non-colinear}\; \iff \exists \triangle ABC.$

For example, see this post.

At any rate, in my answer (at the start), I was assuming that you are trying to both define and construct a triangle.

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    No, I was just *constructing*, not *defining*. It's just a start out for a proof. Would it be presumptuous to assume the readers know we aren't talking about the trivial case?2012-11-08
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    It depends on the context - but in my opinion, you are safe with stating exactly what you posted. And yes, adjacent is precisely the word you want. When you asked me to "undelete" what I said, is the content of this answer what you wanted me to undelete?2012-11-08
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It does sound a bit weird, but I guess it's acceptable since it doesn't seem ambiguous.

How about "extend $\overline{CB}$ past $B$" instead?

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    But "past B" could also (in some way) imply it can "past C" as well2012-11-08
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    "past $B$" seems pretty unambiguous to me. From my experience it's a rather standard phrase.2012-11-08
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    EuYu: I agree with jak. I think that extend "past B" is a bit ambiguous, at least no less ambiguous than what jak has written. jak: I think that your directions are fine. Perhaps I'm overlooking something, but is seems okay to me.2012-11-08
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    jak, at any rate, your use of adjacent is correct,2012-11-08
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    Is it awkward though? Was it easy to interpret what i wanted to say without the accompanied diagram?2012-11-08
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    @jak I think it ultimately comes down to personal preference. I found it a bit weird, but amWhy thinks it's fine. Also, since it's your first choice of wording, clearly it's not awkward to you. As long as it's unambiguous then I would say it's fine.2012-11-08
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    jak, it didn't strike me as awkward. It doesn't specify any particular triangle (in terms of the measure of its angles or the length of its sides) but it does seem to capture the construction of *some* triangle.2012-11-08
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    @amWhy, is there a triangle such that my wording won't work?2012-11-08
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    Sorry, but isn't a triangle by definition are formed by three noncolinear points?2012-11-08
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    I think we're all making this way more complicated than it needs to be.2012-11-08
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    @amWhy, ah okay I seee what you mean2012-11-08
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    @amWhy, could you "undelete" what you said?2012-11-08