Abstract: The stability of the triangle, a description of its determinacy, is a characterization of the quantitative relation in its“pure form” that is unique of a triangle. As a geometric theorem, it can be proven by use of the relations of the three sides of a triangle. Students’ learning of the triangle’s stability has to gone through three successive abstract cognitive stages, namely the qualitative description, logical demonstration and quantitative characterization. In order to help develop the core mathematical competencies in students, different stages of learning in primary school, junior and senior middle school have dif- ferent focus of teaching orientations.