Change the orientation by dragging the shape by a vertex. Describe the position and orientation of the resulting image in relation to the original shape. Now consider the same tasks using other transformations. Discussion Dynamic geometry software allows students to visualize a transformation by manipulating a shape and observing the effect of each manipulation on its image. By focusing on the positions, side lengths, and angle measures of the original and resulting figures, middle-grades students can gain new insights into congruence.
Transformations can become an object of study in their own right.
Teachers can ask students to visualize and describe the relationship among lines of reflection, centers of rotation, and the positions of preimages and images. Using the interactive figure, students might see that the result of a reflection is the same distance from the line of reflection as the original shape. In a rotation, students might note that the corresponding vertices in the preimage and image are the same distance from the center of rotation and all the angles formed by connecting the center to the corresponding vertices are congruent in the image and the preimage.