  Let $G$ be a complete convex geometric graph whose vertex set $P$ forms a
convex polygon $C$, and let $F$ be a family of subgraphs of $G$. A blocker for
$F$ is a set of edges, of smallest possible size, that contains a common edge
with every element of $F$. Previous works determined the blockers for various
families $F$ of non-crossing subgraphs, including the families of all perfect
matchings, all spanning trees, all Hamiltonian paths, etc.
  In this paper we present a complete characterization of the family $B$ of
blockers for the family $T$ of triangulations of $C$. In particular, we show
that $|B|=F_{2n-8}$, where $F_k$ is the $k$'th element in the Fibonacci
sequence and $n=|P|$.
  We use our characterization to obtain a tight result on a geometric
Maker-Breaker game in which the board is the set of diagonals of a convex
$n$-gon $C$ and Maker seeks to occupy a triangulation of $C$. Namely, we show
that in the $(1:1)$ triangulation game, Maker can ensure a win within $n-3$
moves, and that in the $(1:2)$ triangulation game, Breaker can ensure a win
within $n-3$ moves. In particular, the threshold bias for the game is $2$.
