In this lesson, students begin to see that translations, rotations, and reflections preserve lengths and angle measures, and for the first time call them rigid transformations. In earlier lessons, students talked about corresponding points under a transformation. Now they will talk about corresponding sides and corresponding angles of a polygon and its image.
As students experiment with measuring corresponding sides and angles in a polygon and its image, they will need to use the structure of the grid (MP7) as well as appropriate technology, including protractors, rulers, and tracing paper.
- Comprehend that the phrase “rigid transformation” refers to a transformation where all pairs of “corresponding distances” and “corresponding angle” measures in the figure and its image are the same.
- Draw and label a diagram of the image of a polygon under a rigid transformation, including calculating side lengths and angle measures.
- Identify (orally and in writing) a sequence of rigid transformations using a drawing of a figure and its image.
Let’s compare measurements before and after translations, rotations, and reflections.
- I can describe the effects of a rigid transformation on the lengths and angles in a polygon.
When part of an original figure matches up with part of a copy, we call them corresponding parts. These could be points, segments, angles, or distances.
For example, point \(B\) in the first triangle corresponds to point \(E\) in the second triangle. Segment \(AC\) corresponds to segment \(DF\).
A rigid transformation is a move that does not change any measurements of a figure. Translations, rotations, and reflections are rigid transformations, as is any sequence of these.