Technology isn't required for this lesson, but there are opportunities for students to choose to use appropriate technology to solve problems. In rigid motion, the position or orientation of the set as a whole changes without the distance of the line segments changing. In a triangle, for example, the set consists of the three points and three line segments that combine to form the triangle. In math, a set is a group of objects or elements. In a subsequent unit, students will prove that the shortest path between a point and a line is along the perpendicular. Rigid motion is a movement of a set so that the distance between points doesn’t change. Students make arguments and critique the arguments of others when they compare strategies for finding sequences of rigid transformations that take one figure onto another (MP3).Īt this point, students take the distance between a point and a line as the distance along the perpendicular as a definition. This idea builds toward the concept of transformations as functions while preparing students to reason about sequences of transformations in addition to single motions.
Students determine that different sequences of rigid motions can result in the same image, and when sequences are reordered, they sometimes don’t result in the same image. While students may mention them, rotations do not get defined until a subsequent lesson. This video describes the difference between rigid motion and non-rigid motion, a concept you learn about in a high school Geometry course. The study of coordinate geometry is reserved for a subsequent unit. Students work on an isometric grid to push them toward needing precise definitions.ĭuring this lesson, students focus on translations and reflections. In this lesson, students study transformations on a grid, then in subsequent lessons in this unit, students learn precise definitions for rigid motions that apply off the grid. Students also recall that the definition of congruent is any two figures where there is a sequence of translations, rotations, and reflections that takes the first figure onto the second.
These motions and the sequences of the motions, called rigid transformations, affect the entire plane, but students generally focus on a single figure and its image (the result of a transformation). This lesson builds on prior knowledge about congruence to reinforce the idea that the rigid motions, translations, reflections, and rotations preserve distances and angles.
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