However, this choice of grid also makes it easier to reason about the reflections if they understand the descriptions of rigid motions indicated in 8.G.3. Also providing a challenge is the fact that the grids have been drawn so that they are aligned with the diagonal of the rectangles rather than being aligned with the vertical and horizontal directions of the page. This means that students need to approximate and this provides an extra challenge. Note that the vertices of the rectangles in question do not fall exactly at intersections of the horizontal and vertical lines on the grid. The task is intended for instructional purposes and assumes that students know the properties of rigid transformations described in 8.G.1. Note that a line of symmetry can be thought of as a transformation that shows a figure is congruent to itself in a non-trivial way. This leads naturally to the last part of the question: lines through a diagonal are lines of symmetry for a square (but not a non-square rectangle). Moreover, this "displacement" of the rectangle becomes smaller and smaller as the rectangle becomes closer to being a square. The examples show that the reflected image looks like a rotation of the original rectangle about its center point. In the case of reflecting a rectangle over a diagonal, the reflected image is still a rectangle and it shares two vertices with the original rectangle. The goal of this task is to give students experience applying and reasoning about reflections of geometric figures using their growing understanding of the properties of rigid motions.