A Re-Examination of the Area formula of triangles as an invariant of Euclidean geometry

유클리드 기하의 고유한 성질로서의 삼각형 넓이 공식에 대한 재음미

This study suggests that it is necessary to prove that the values of three areas of a triangle, which are obtained by the multiplication of the respective base and its corresponding height, are the same. It also seeks to deeply understand the meaning of Area formula of triangles by exploring some questions raised in the analysis of the proof. Area formula of triangles expresses the invariance of congruence and additivity on one hand, and the uniqueness of parallel line, one of the characteristics of Euclidean geometry, on the other. This discussion can be applied to introducing and developing exploratory learning on area in that it revisits the ordinary thinking on area.