Isometry - length is preserved - the figures are congruent.
Direct Isometry - orientation is preserved - the order of the lettering in the figure
     and the image are the same, either both clockwise or both counterclockwise.
Opposite Isometry - orientation is not preserved - the order of the lettering is reversed,
     either clockwise becomes counterclockwise or counterclockwise becomes clockwise.

 

Line Reflection	Point Reflection	Translations	Rotations	Dilations
Opposite isometry	Direct isometry	Direct isometry	Direct isometry	NOT isometry. Figures are similar.
Properties preserved: 1. distance 2. angle measure 3. parallelism 4. colinearity 5. midpoint	Properties preserved: 1. distance 2. angle measure 3. parallelism 4. colinearity 5. midpoint	Properties preserved: 1. distance 2. angle measure 3. parallelism 4. colinearity 5. midpoint	Properties preserved: 1. distance 2. angle measure 3. parallelism 4. colinearity 5. midpoint	Properties preserved: 1. angle measure 2. parallelism 3. colinearity 4. midpoint Lengths not same.
Reverse Orientation (letter order changed)	Same Orientation (letter order the same)	Same Orientation (letter order the same)	Same Orientation (letter order the same)	Same Orientation (letter order the same)
Notation:	Notation:	Notation:	Notation:	Notation:

 

Glide Reflection Opposite isometry Properties preserved: 1. distance 2. angle measure 3. parallelism 4. colinearity 5. midpoint Reverse Orientation (letter order changed)

 

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Topic Index | Geometry Index | Regents Exam Prep Center Created by Donna Roberts