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25 Cards in this Set
- Front
- Back
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A transformation is... |
a one-to-one correspondence between two sets of points. |
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An isometry is...
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a transformation that preserves distance and angle measure. |
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A reflection is... |
a transformation in which each point, P, reflected through line is P itself if P lies on line l; else it is the point P’ (read ‘p prime’) such that PP’ is the perpendicular bisector of line l . (Mirror image.) |
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A translation is... |
the composite of two successive reflections through parallel lines. (Figure looks like it has been slid without turning.) |
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A rotation is...
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the composite of two successive reflections through intersecting lines. (Figure looks like it has been slid and turned.) |
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A dilation is... |
a transformation in which angle measure is preserved, and all distances are of the same proportion. (Figure is made larger or smaller.) |
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Definition of congruence by transformation. |
Two figures are congruent if there is an isometry such that one figure is the image of the other. |
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A glide reflection is...
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the composite of a translation (glide) and a reflection (flip) in a line parallel to the direction of the translation. (Footprints in the sand can be formed this way.) |
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A figure has rotation symmetry with respect to a point... |
iff it coincides with its rotation image through less than 360° about the point. |
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n-fold rotation symmetry |
A figure has n-fold rotation symmetry iff the smallest angle through which it can be turned to look exactly the same is 360/n |
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reflection (line) symmetry
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A figure has reflection (line) symmetry with respect to a line iff it coincides with its reflection image through the line. |
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translation symmetry
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A figure has translation symmetry iff it coincides with a translation image. |
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magnitude of translation
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The distance between a point of the original figure and its translation. |
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magnitude of rotation
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The angle through which a point of the original figure turns to coincide with its rotation image |
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A one-to-one correspondence between two sets of points is called…
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a transformation. |
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A transformation that preserves distance and angle measure is…
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an isometry. |
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A mirror image is…
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a reflection. |
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The image achieved by the composite of two successive reflections through parallel lines is…
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a translation. |
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The composite of two successive reflections through intersecting lines is…
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a rotation. |
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The transformation in which angle measure is preserved, and all distances are of the same proportion is…
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a dilation. |
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The transformation achieved by the composite of a translation and a reflection in a line parallel to the direction of the translation is…
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a glide reflection. |
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The distance between a point of the original figure and its translation is called…
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the magnitude of translation. |
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The angle through which a point of the original figure turns to coincide with its rotation image is called…
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the magnitude of rotation. |
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Examples of transformations described in Ch 8 that are isometries are... |
reflection, glide reflection, translation, rotation. |
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If a figure has been rotated, the point of rotation can be found by... |
1. Connect a point P with its image, P'.
The intersection of the two bisectors is the point of rotation. |
