  We introduce an generalization of the theta divisor to the theory of
holomorphic triples on a smooth projective curve $X$. We show that a given
triple $T=(E_1 \to E_0)$ is $\alpha$-semistable iff there exists an orthogonal
tripe $S=(F_1 \to F_0)$ with given numerical invariants. This yields globally
generated theta line bundles on the moduli space of semistable triples.
