Instructional Implications Review the definition of each of the rigid transformations: translations, reflections, and rotations. To develop an intuitive understanding of rigid transformations, allow the student to experiment with a variety of transformations using transparent paper or interactive websites such as http://www.mathsisfun.com/geometry/, http://www.mathopenref.com/translate.html or http://www.shodor.org/interactivate/activities/TransmographerTwo/.
Be sure the student understands that:
 A translation is a transformation of the plane. A transformation along a vector v assigns to each point, P, in the plane an image point, , so that the distance from to P corresponds to the magnitude (length) of vector v and the direction of from P corresponds to the direction of vector v. Use grid paper to illustrate translations of points and to demonstrate the relationship between a point, its image, and the vector that defines the translation. Then illustrate translations of more complex figures such as segments, angles, and polygons.
 A reflection is a transformation of the plane. A reflection across line m (the line of reflection) assigns to each point not on line m, a point that is symmetric to itself with respect to line m (e.g., m is the perpendicular bisector of the segment whose endpoints are the point and its image). Also, a reflection assigns to each point on line m the point itself. Use grid paper to illustrate reflections of points and to demonstrate the relationship between a point, its image, and the line of reflection. Then illustrate reflections of more complex figures such as segments, angles, and polygons.
 A rotation is a transformation of the plane. Each point in the plane is rotated a specified number of degrees (given by the degree of rotation) either clockwise or counterclockwise (indicated by the sign of the degree of rotation) about a fixed point called the center of rotation. Use a unit circle to illustrate rotations of points about the origin. Then illustrate rotations of more complex figures such as segments, angles, and polygons.
After introducing each rigid motion through the transformation of points, introduce more complex figures such as segments, angles, and polygons. Emphasize the basic properties of rigid motions:
 Lines are taken to lines, and line segments to line segments of the same length.
 Angles are taken to angles of the same measure.
 Parallel lines are taken to parallel lines.
Discuss how these properties ensure that the image of a figure under a rigid motion is always congruent to the preimage.
Provide additional opportunities to experiment with translations using transparent paper and to verify experimentally the properties of translations, reflections, and rotations. 
Instructional Implications Provide additional opportunities to experiment with rigid motions using transparent paper and to verify experimentally the properties of translations, reflections, and rotations. Emphasize the basic properties of rigid motions:
 Lines are taken to lines, and line segments to line segments of the same length.
 Angles are taken to angles of the same measure.
 Parallel lines are taken to parallel lines.
Discuss how these properties ensure that the image of a figure under a rigid motion is always congruent to the preimage. Model using appropriate mathematical terminology to describe rigid motion and explain the properties.
