A puzzle of vertices

In a book of geometry of the school there is the next puzzle: place the next nine triangles to form only one such that the vertices that join have the same symbol.

I solved it through an naïve analysis but I think that this can be solved with graph theory(although I only have an idea of what is graph theory).

Is graph theory a good approach or perhaps there is a most natural background to the problem?

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The straightforward analysis is by far the simplest method, it only takes about 4 steps. I doubt that there would be any graph theoretic interpretation (at least one which would simplify the problem). –  EuYu Mar 13 '13 at 6:41
@EuYu thanks! but at least there exist a graph theoric approach that solve the problem? –  Eduardo Alan Dávalos Peña Mar 13 '13 at 6:49
Of course I can't say there doesn't exist one, but there isn't an immediately obvious way to formulate the problem. I guess I mean to say that this problem doesn't seem naturally graph theoretic. –  EuYu Mar 13 '13 at 6:56
@EuYu then wich setting would be the more natural? –  Eduardo Alan Dávalos Peña Mar 13 '13 at 7:00
I'm a bit confused as to why you think that there must be a natural setting for a problem. It just seems to me that this problem can be simply deduced, there isn't any real need for mathematical machinery. Are you unhappy with your analysis? –  EuYu Mar 13 '13 at 7:02
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