This study aimed to analyze the structure of students’ argumentation while solving a geometry problem. As a qualitative inquiry, the study examined the structural and cognitive components involved in the development of students’ argumentation throughout problem solving. Participants were three groups of three eleventh-grade students from a county in Tehran Province. The groups were organized from among 15 students based on similarities in their reasoning patterns, and each group then solved the same geometry problem. Data were collected through video recordings, transcripts of group discussions, field notes, and students’ written work, enabling reconstruction of their reasoning processes and interactions. Data analysis was conducted using an integrated analytical framework combining Toulmin’s model of argumentation and Balacheff’s cK¢ model. The findings revealed that students’ argumentation was dynamic and multilayered, emerging through the interaction of components such as data, claims, warrants, backing, control, rebuttals, operators, and representational systems. Four forms of reasoning were identified: visual reasoning, inductive reasoning, abductive reasoning, and informal deductive reasoning. Among these, abductive and informal deductive reasoning played the most influential role in supporting students’ movement toward formal deductive argumentation. Furthermore, the coordination of multiple representations—particularly the transformation of visual and numerical representations into algebraic relationships—was essential for constructing coherent argumentation. The activation of control and rebuttal components, together with collaborative interactions, enabled students to refine their reasoning, revise their arguments, and strengthen the validity of their conclusions. The findings may contribute to the revision of mathematics curricula, the design of instructional activities, and inform future research.