This book is the result of my master's research on the theme Significant ways of acting and thinking for the self-training of teachers who teach mathematics, in relation to the teaching of plane geometry. It is aimed more specifically at future teachers on undergraduate mathematics courses, teachers who teach in basic education and researchers interested in the study of plane geometry. Teachers who are already working in schools will certainly find in this book a theoretical exposition, a source for reflections on their practice with regard to the teaching and learning of plane geometry, which will translate into new work proposals, guiding teaching action given the fact that it was identified, in the course of the research, a certain limitation of the concepts that involve such content.