Digital technologies for mathematics education are continuously developing. Still, much remains unknown about how students use these tools and how this affects learning. For example, tablets nowadays come with multi-touch options that allow for a more embodied approach to geometry education, compared to mouse interactions. However, little is known about how students use these opportunities to develop bodily-based conceptualizations of geometric concepts in a touch-based dynamic geometry environment (DGE). The aim of this study was to investigate students' dragging schemes from an embodied instrumentation perspective and to identify the types of embodied-dragging schemes that the students use, while transforming one type of parallelogram into another. Fifty-seven 11-year-old students worked on a task on transforming a given parallelogram into a rectangle and next into a square, using a tablet-enabled DGE. Results showed that students used three types of embodied dragging schemes: (a) action-perception dragging guided by perceived prototypical images of shapes, (b) sequentially-coordinated dragging based on initial perception and then utilizing the affordances of the artefacts, and (c) adaptive dragging, effectively integrating action-perception loops and geometrical properties. In schemes of types (b) and (c), geometric properties of the constructed shapes emerged and guided students' action-perception loops. As a conclusion, this description informs teachers, textbook authors, and designers of digital assessment on how to design student activities. From a theoretical perspective, the embodied instrumentation lens provided a fruitful approach to study student-tool interactions in geometry that does justice to the bodily foundations of mathematical cognition.