A Dynamic Model to Engage Students in the Triangle’s Inherent Similarity

Abstract

This paper presents a dynamic model created with GeoGebra to explore and demonstrate relationships inherent in triangles, particularly those involving side partitions formed by the triangle's altitudes. These relationships, while not commonly featured in high school geometry curricula, offer a unique opportunity for students to investigate mathematical theorems dynamically. The paper examines the relationships a₁b₁c₁=a₂b₂c₂ and a₁²+b₁²+c₁²=a₂²+b₂²+c₂², providing an interactive GeoGebra model, formal proofs, and suggested materials for classroom use.