The aim of this research was to examine mathematics teachers' performances in defining special types of quadrilaterals, identifying their family and hierarchically classifying them. In this vein, 33 of 58 primary school mathematics teachers working in the province of Yozgat, Turkey were voluntarily recruited for this survey, and they were asked to complete a data collection form consisting of three open-ended questions. In the first question, participants were asked to define the special types of quadrilaterals. In the second question, teachers were asked to recognise kites, trapezoids, parallelograms, rectangles and rhombuses among 15 quadrilaterals. Finally, participants were prompted to make a hierarchical classification of the special types of quadrilaterals. The results of this study illustrated that while 20 mathematics teachers could define a kite hierarchically, only 1 of the sample could hierarchically define a trapezoid. In addition, participants encountered difficulties not only in determining the kite and trapezoid family, but also in demonstrating the relations of kite-rhombus, trapezoid-parallelogram and trapezoid-rectangle quadrilaterals. Hence, in-service training programs for primary school mathematics teachers should be organized to improve content knowledge of geometry in general and quadrilaterals in particular.