The invariant mass method is used to identify the $^8$Be and $^9$B nuclei and Hoyle state formed in dissociation of relativistic nuclei in a nuclear track emulsion. It is shown that to identify these extremely short-lived states in the case of the isotopes $^9$Be, $^{10}$B, $^{10}$C, $^{11}$C, $^{12}$C, and $^{16}$O, it is sufficient to determine the invariant mass as a function of the angles in pairs and triples of He and H fragments in the approximation of the conservation of momentum per nucleon of the parent nucleus. According to the criteria established in this way, the contribution of these three unstable states was evaluated in the relativistic fragmentation of the $^{28}$Si and $^{197}$Au nuclei.
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