  In this paper, we will study compatible triples on Lie algebroids. Using a
suitable decomposition for a Lie algebroid, we construct an integrable
generalized distribution on the base manifold. As a result, the symplectic form
on the Lie algebroid induces a symplectic form on each integral submanifold of
the distribution. The induced Poisson structure on the base manifold can be
represented by means of the induced Poisson structures on the integral
submanifolds. Moreover, for any compatible triple with invariant metric and
admissible almost complex structure, we show that the bracket annihilates on
the kernel of the anchor map.
