Exploring synthetic geometry problem-solving methods through auxiliary construction analysis using technology tools

This paper proposes proof methods for synthetic geometry problem by dividing it into a process of observing geometric properties of auxiliary constructions(auxiliary lines and auxiliary circles) drawn using technology tools without logical proof and a process of logically proving the observes geometric properties. Through this method, students can approach problems more easily and the utilization of technology tools is maximized, so each student can solve geometry problems that were difficult to solve using traditional methods. In addition, it can be expected that this method will play a meaningful role in improving students' logical thinking abilities by being able to solve problems with only basic geometry knowledge without using difficult geometric theorems.