Glide Reflection Worksheet
1. Using Geometer's Sketchpad, bring up the sketch titled "Glide Reflection". Follow the instructions at the top to demonstrate a glide reflection of the given triangle (here is a link to the sketch
Using the Sketchpad software, connect the corresponding points of triangles ABC and A'''B'''C'''. Where do you suppose the midpoints of the lines formed will be?
2. Highlight each line individually and construct the midpoint to check your conjecture. What do you observe? Write down an argument as to why your observation should be always be true.
3. Given that the two congruent figures below are glide reflection images of each other, draw three lines (m, n and p) of reflection that could be used to accomplish the glide reflection. Include the reflected triangles in your drawing. Refer to Sketchpad "Glide Reflection" file for a means of working with Sketchpad to check and/or find an answer.
Are the lines you drew unique? Could others be used to obtain the same result? Explain.
Discussion and Extension
1. Explain whether the orientation of a figure changes under a glide reflection.
2. In general, would you expect to be able to rewrite the composition of two different glide reflections as a reflection, a rotation, a translation, or another glide reflection? Use orientation in your argument.
3. In the glide reflection, do you think it matters whether the translation is performed first, before the reflection, or whether the reflection is performed first, before the translation? Explain.
4. Explain, giving examples, whether or not the order in which transformations are done matters in general in determining the final image.