High School: Geometry
4. Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments.
Students should be able to recognize and visualize transformations of geometric shapes and not only reflect, rotate, and translate shapes, but also combine these three different transformations. By defining and describing these transformations in reference to angles, circles, lines and line segments, students should gain a deeper understanding of these transformations and when these operations apply to real world situations.
Show how rotations, reflections, and translations are drawn, but also to use polygons in order to perform a few of these transformations. Then, explain how each step meshes with the definition of that transformation. The more examples, the merrier!
Also, remind students that when a geometric shape undergoes a rigid transformation, its angles cannot change. Rigid transformations do not affect length, area, or angle measure of a geometric shape. They do, however, affect your flexibility in yoga class.
Students should use the three transformations listed to explore and prove geometric properties. The best way to analyze these transformations in terms of angles, circles, line segments, and perpendicular and parallel lines is to consider each individually.
For example, your students are driving (and definitely not texting) and approaching a four-way intersection. The two streets will be perpendicular to one another. If we picture a line down the middle of one of the streets, either horizontally or vertically, and we imagine folding the streets over each other, we will have a reflection transformation.
The angles and the angles are all mirrored, but due to the 90° angles all around, they are congruent either way. Of course, actually folding streets over would be some crazy Inception-style infrastructure, but you get the point.