A well-known result of \textit{C. M. Ringel} [Tame algebras and integral quadratic forms. Lect. Notes Math. 1099 (1984; Zbl 0546.16013)] states that a representation-directed algebra is representation-finite. Moreover, if it possesses a sincere indecomposable module then the dimension vector map furnishes a bijection between the isomorphism classes of the indecomposable modules and the positive roots of the Tits (equivalently, Euler) form which is in addition weakly positive. These results have been extended to quasi-hereditary algebras by \textit{B. Deng} [J. Algebra 239, No. 2, 438-459 (2001; Zbl 0997.16005)]. In the paper, the above mentioned results are generalized to standardly stratified algebras. We recall briefly the definition of standardly stratified algebras. For an ordering \(S_1,\dots,S_n\) of the simple modules over an algebra \(A\) we denote by \(\Delta_i\) the maximal factor of the projective cover of \(S_i\) with no composition factors \(S_j\) for \(j=i+1,\dots,n\). We call \(\Delta_1,\dots,\Delta_n\) the standard modules. The algebra \(A\) is called standardly stratified (with respect to the given ordering of the simple modules) if every projective \(A\)-module is \(\Delta\)-good, i.e.~belongs to the smallest extension closed subcategory of the category of \(A\)-modules containing the standard modules. The authors prove that if the category of \(\Delta\)-modules is directing (there are no cycles in the module category involving only \(\Delta\)-modules), then there is only a finite number of the isomorphism classes of the indecomposable \(\Delta\)-good modules. Moreover, if in addition there is an omnipresent (every standard module appears as a composition factor) indecomposable \(\Delta\)-good module and the projective dimension of every standard module is at most \(2\), then the Tits quadratic form \(q_\Delta\) associated with the standard modules in a usual way is weakly positive and there is a bijection between the isomorphism classes of the indecomposable \(\Delta\)-good modules and the positive roots of \(q_\Delta\) given by the dimension vector map. In fact, the first of the above mentioned results is proved in a more general context of stratifying systems. We also add that stratifying systems are widely used in the proofs.