This paper provides a framework aimed to classify level of realizing geometric invariants in proving process with the support of dynamic geometry environment. Based on these levels, the authors lay emphasis on the role of realizing geometric invariants in finding the strategies to solve a problem. In particular, students have better understanding of transformation groups while they are working with geometric invariants of different geometries. As a result, they can use appropriate realized invariants in order to collect the data, formulate the conjecture, produce arguments, combine the arguments and wirte a formal proof.