We study connections between structure tensors of almost contact metric manifold $M$ and the canonical almost Hermitian structure on its linear extension $M\times\mathbb R$. We obtain a complete system of structure equations of the linear extension of quasisasakian manifold. We study connection between curvature identities of the linear extension of quasisasakian manifold and properties of curvature of linear extension of quasisasakian manifold in the two-dimensional direction determined by the bivector $\xi\times X$, where $\xi$ is the structure tensor of quasisasakian structure.