Computers have been trying to make their way into education, because they can allow learners to manipulate abstract notions and explore problem spaces easily. However, even with the tremendous potential of computers in education, their integration into formal learning has had limited success. This may be due to the fact that computer interfaces completely rupture the existing tools and curricula. We propose paper interfaces as a solution. Paper interfaces can be manipulated and annotated yet still maintain the processing power and dynamic displays of computers. We focus on geometry, which allows us to fully harness these two interaction modalities: for example, cutting a complex paper shape into simpler forms shows how to compute an area. We use a camera-projector system to project information on pieces of paper detected with a 2D barcode. We developed and experimented with several activities based on this system for geometry learning, however, we focus our presentation on one activity addressing symmetry. This activity is based on a sheet where a part of its content is scanned, and then reprojected according to one or more symmetry axes. Such a sheet is used to illustrate, in real time, how a symmetric drawing is constructed. Anything in the input area can be reflected: ink paper shapes, or physical objects. We show how the augmented sheets provide an easy solution for teachers to develop their own augmented reality activities by reporting on the collaboration with three teachers. These teachers successfully used the activities in their classes, integrating them in the normal course of their teaching. We also relate how paper interfaces let pupils express their creativity while working on geometry.