Many of them reflect the shape as if it was a vertical line. Reflection over the y = x line causes them great trouble. The coordinate rules make sense and are often easy for students to memorize but it seems that the most difficult area for students with reflection is working with non-vertical or non-horizontal lines of reflection. Reflection seems to come easy to students because of its relationship to symmetry. Two figures are CONGRUENT if and only if one can be obtained from the other by one or a sequence of rigid motions. Congruence gains a new definition than we have used in the past. Performing an isometric transformation or a sequence of them prepare us for congruence. If we can determine a sequence of isometric transformations that maps the pre-image exactly onto the image then they are congruent. (8) The student will demonstrate how some composite transformations are not commutative. (7) The student will be able to identify a transformation by its coordinate rule and then apply it to transform the shape. (6) The student will be able to describe which single transformation is the result of two reflections over intersecting lines. (5) The student will be able to describe which single transformation is the result of two reflections over parallel lines. (4) The student will be able to determine the sequence of transformations performed between a given pre-image and image. (3) The student will be able to perform a sequence of transformations. (2) The student will be able to construct a rotation, a reflection and a translation. (1) The student will be able to perform a reflection, a rotation, and a translation. This emphasizes the properties and definitions of transformations while preparing students for congruence. These are not the only patterns to be found students should be able to given a pre-image and a final image and determine one possible sequence of transformations that maps one onto the other. We investigate the relationships found by reflecting over two parallel lines and reflecting over two intersecting lines. We also extend single transformations to composite transformations of two or more motions in the plane. This is a continuation from G.CO.4 where we defined the motions and now we begin to actually perform the transformations. This is objective is all about performing the transformation. Specify a sequence of transformations that will carry a given figure onto another. Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure using, e.g., graph paper, tracing paper, or geometry software. High School Geometry Common Core G.CO.A.5 - Sequences of Transformations - Patterson
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