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Kaleidoscopes, Hubcaps, and Mirrors (Part A)
Enrichment Activities
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Objectives of this Unit
| Understand important properties of symmetry | Recognize and describe symmetries of figures |
| Perform symmetry transformation of figures, including reflections, translations, and rotations | Write coordinate rules for specifying the image of a general point (x,y) under particular transformations |
| Combine transformations to find a single transformation that will achieve the same result |
Vocabulary
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Congruent Figures | Two figures are congruent if one is an image of the other under a translation, a reflection, a rotation, or some combination of these transformations. Two figures are congruent if you can flip, slide, or turn one figure so that it fits exactly on the other. |
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Kaleidoscope | A tube containing colored beads or pieces of glass and carefully placed mirrors. When a kaleidoscope is held to the eye and rotated, the viewer sees colorful, symmetric patterns. |
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Line Reflection | A transformation that matches each point on a figure with its mirror image over a line. |
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Reflectional Symmetry | A figure or design has reflectional symmetry if you can draw a line that divides the figure into halves that are mirror images. The line that divides the figure into halves is called the line of symmetry. |
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Rotation | A transformation that turns a figure counter-clockwise about a point. |
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Rotational Symmetry | A figure or design has rotational symmetry if it can be rotated less than a full turn about a point to a position in which it looks the same as the original. |
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Symmetry | An object or design has symmetry if part of it is repeated to create a balanced pattern. |
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Tessellation | A design made from copies of a basic design element that cover a surface without gaps or overlaps. Tessellations have translational symmetry. |
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Transformation | A geometric operation that matches each point on a figure with an image point. A symmetry transformation produces an image that is identical in shape and size to the original figure. |
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Translation | A transformation that slides each point on a figure to an image point a given distance and direction from the original point. If you drew line segments from two points to their respective image points, the segments would be parallel and they would have the same length. |
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Translational Symmetry | A design has translational symmetry if it can be created by copying and sliding a basic shape in a regular pattern. Translational symmetry is found in wallpaper designs and tessellations. |