Let A and B be unital algebras over a commutative ring R, and M be a unital $\,B)-bimodule and $\alpha,\beta$ be algebra homomorphisms of A. This paper determines all homomorphisms and hence all automorphisms of the triangular algebra Tri(A,M,B) and using the characterizations, it is shown that under some conditions, every $(\alpha,\beta)$-Jordan derivation from the triangular algebra Tri(A,M,B) into itself is an $(\alpha,\beta)$-derivation. As a consequence several known results is extended.
