This is the first i-Math in a four-part series of i-Maths entitled Symmetries and Their Properties. In this first i-Math you will investigate rotational symmetry. Fix a center, turn, and you have a rotation. Many objects in nature—flowers, starfish, and crystals—and objects we use every day, such as wheels, CDs, and drinking glasses, have rotational symmetry. Here, you will learn about the mathematical properties of rotations and have an opportunity to make your own designs.
2. Represent transformations in the plane using, e.g., transparencies and geometry software; describe transformations as functions that take points in the plane as inputs and give other points as outputs. Compare transformations that preserve distance and angle to those that do not (e.g., translation versus horizontal stretch).
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3. Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections that carry it onto itself.
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4. Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments.
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