1. Isometries Page 15-19

2. Isometry – A transformation in a plane that results in an image that is congruent to the original object. Which transformations are isometries? 1.Line reflections 2.Point reflections 3.Translations 4.Rotations 5.Glide Reflection Dilations are NOT isometries. They do not preserve distance!!

3. Direct Isometry – An isometry that preserves orientation. Which transformation are direct isometries? 1.Point reflections 2.Translations 3.Rotations

4. Point reflection in the origin.

5. Translation:

6. Rotation:

7. Opposite Isometry – An isometry that does not preserve orientation. Which transformation are opposite isometries? 1.Line reflections 2.Glide reflections

8. Glide Reflection:

9. Compositions with Isometries **An even number of opposite isometries results in a direct isometry **An odd number of opposite isometries results in an opposite isometry Direct isometry DD Opposite isometry OD DD Direct isometry OD OD OD

10. Page 17

11. Page 18