The main purpose of this work is to rescue the important concepts in geometric constructions. Concepts that are being progressively forgotten by Brazilian curriculums in schools. First, we want to present the difficulties that high school teachers might face when they will try to formalize concepts like the possibility or not to construct some figures in the Euclidean plane, especially those who have not studied advanced math courses at undergraduation. We comment on the main problems of antiquity that led mathematicians to new discoveries properties, we present geometric constructions as well as an algebraic description of these geometric constructions. The idea is that through abstract algebra we can present arguments about the possibility or impossibility of such constructions. In this work, we will comment that abstract algebra will help teachers to validate some arguments that involves the possibility or not to construct some figures as well as to enlarge high schools teachers culture, not trying to make them experts in the subject.