  In this paper, we will see that the symplectic creed by Weinstein "everything
is a Lagrangian submanifold" also holds for Hamilton-Poincar\'e and
Lagrange-Poincar\'e reduction. In fact, we show that solutions of the
Hamilton-Poincar\'e equations and of the Lagrange-Poincar\'e equations are in
one-to-one correspondence with distinguished curves in a Lagrangian submanifold
of a symplectic manifold. For this purpose, we will combine the concept of a
Tulczyjew triple with Marsden-Weinstein symplectic reduction.
