Basic geometric equalities and problem-solving: Linear elements

Abstract

This paper presents some equalities that we consider useful for the resolution of general high school level geometry problems. The presented geometric equalities involve only linear elements. The objective of this work is to monitor, on a very small scale, the skills and knowledge acquired by students in the eleventh year of school in an Italian region named Apulia. This has been done by mean of different exercises where 23 students were asked to recognize and combine the equalities presented. Results are reported and discussed.