Students of the extended abstract in proving Lobachevsky's parallel lines theorem

The highest quality of the students in proving the theorem was extended abstract. One of the theorems that was difficult to determine was Lobachevsky's parallel lines. The purpose of this study was to describe the characteristics of extended abstract level students in proving the Lobachevsky parallel lines theorem. This was part of research development. This stage was the student analysis phase. The subjects of this study were 21 Mathematics Education Pre-service teachers who were taking Geometry courses. The instrument of this study was the researchers themselves with the help of task sheets and interview guides. Data was collected through task-based interviews. Qualitative data analysis techniques with fixed comparison techniques. The results of this study were that students were able to understand the axiom "through a point outside the line g, there were at least two lines parallel to g". This axiom was used to prove the Nonmetrical Theorem. Also, students were able to prove that through point T which was not located at line g, there were not so many lines parallel to g. Students were able to compare the deductive structure of Lobachevsky's Geometry with Euclid's Geometry. The conclusion of this study was that extended abstract students were able to present several elements and pass interdependence between one another, so that it becomes an integrated entity. He can generalize to new structures.