Is the word "adjacent" being used correctly in this geometry problem? 
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"
 A: 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.
A: 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?
