Perceiving and interpreting invariants is a complex task for a nonexpert geometry student, as various studies have shown. Nevertheless, having students work through particular kinds of activities that involve perception and interpretation of invariants and engage in discussions with classmates, guided by the teacher, can help them learn mathematics. This article presents an activity that can be used in high school geometry and can help students develop the concepts of the premise and the conclusion of a conjecture. This open-ended activity in dynamic geometry can allow for explorations in maintaining dragging, a specific technique that can be useful for generating conjectures. Activities such as this offer students the opportunity to use their prior mathematical knowledge as they enhance their learning, to engage in a physical experience within a dynamic geometry system (DGS), and to build new mathematical knowledge actively, as emphasized in "Principles and Standards for School Mathematics" (NCTM 2000). (Contains 5 figures.)