TEACHING SIMILAR TRIANGLES, HOMOTHETY, QUADRILATERALS, AND CIRCLES IN SECONDARY SCHOOL GEOMETRY: A LITERATURE REVIEW

Abstract

Similar triangles, homothety, quadrilaterals, and circles constitute a core sequence of topics in secondary school plane geometry, yet each presents distinct pedagogical challenges related to students' developmental readiness for formal geometric reasoning. This paper reviews recent literature on teaching methodologies for this topic cluster, drawing primarily on studies published between 2023 and 2025. The review addresses three interconnected themes: the van Hiele model of geometric thinking as a diagnostic and instructional framework, particularly as applied to student misconceptions about quadrilaterals; task-design approaches to introducing homothety and similarity transformations, informed by the Mathematical Working Space framework; and the role of dynamic geometry software, particularly GeoGebra, in supporting conceptual understanding across this topic sequence. Across this literature, a recurring finding is that a substantial proportion of secondary students remain at pre-formal (visualization or early analysis) levels of geometric thinking when engaging with quadrilateral classification and transformation concepts, and that textbook presentation of these topics, particularly homothety, often contains structural inconsistencies that compound these difficulties. The review concludes that effective instruction in this domain requires explicit attention to students' van Hiele level, carefully sequenced task design, and integration of dynamic geometry tools rather than reliance on static diagrams alone.