In Turkey, the content of the geometry course in the Primary School Mathematics Education, which is developed by The Council of Higher Education (YOK), comprises Euclidean and non-Euclidean types of geometry. In this study, primary mathematics teacher candidates compared these two geometries by focusing on Taxicab geometry among non-Euclidean geometries so that they could comprehend Euclidean geometry better. They were asked to perform this comparison through a project-based learning method, due to its student-centered and interdisciplinary nature and association with real life. The findings were collected through the study groups' project reports and the teacher candidates' written opinion statements. By the end of the study period, the teacher candidates involved in the current study discovered that Taxicab geometry was a kind of geometry used in daily life. They further realized that the concept of distance used in real life sometimes emerged as Euclidean distance and sometimes as Taxicab distance. (Contains 19 figures and 1 table.)