1. Geometry 12-5 Symmetry

2. Vocabulary Image – The result of moving all points of a figure according to a transformation Transformation – The rule that assigns to each point of a figure another point in the plane

3. Vocabulary Rigid Transformation, Isometry – The image is congruent to the original figure Nonrigid Transformation – A transformation that does not preserve the size and the shape

4. Translation Translation – An isometry where each point is moved by the same translation vector

5. Translation

6. Rotation Rotation – An isometry in which each point is moved by the same angle measure in the same direction along a circular path about a fixed point

7. Rotation Rotation with Patty Paper

8. Reflection Reflection – An isometry in which each point and its image are on opposite sides and the same distance from a fixed line

9. Reflection

10. Investigation Get your supplies Straight Edge Patty Paper

11. Investigation Draw a polygon and a line of reflection next to it on a piece of patty paper

12. Investigation Fold your patty paper along the line of reflection and create the reflected image of your polygon by tracing it

13. Investigation Draw segments connecting each vertex with its image point. What conclusion can you draw comparing the segments and the line of reflection

14. Investigation Conjecture The line of a reflection is the perpendicular bisector of every segment joining a point in the original figure with its image

15. Vocabulary Reflectional Symmetry – The property that a figure coincides with itself under a reflection (mirror symmetry) Line of Symmetry – The line of reflection of a figure having reflectional symmetry

16. Vocabulary Rotational Symmetry – The property that a figure coincides with itself under some rotation Point Symmetry – The property that a figure coincides with itself under a rotation of 180°

17. Vocabulary N-Fold Rotational Symmetry – When the angle of rotation can be expressed as 360/n, for a positive value of n

18. Sample Problems

24. Homework Pages 664 – 666 1 – 12 (draw diagrams), 25 – 32, 58 – 60

25. Honors Homework Pages 664 – 666 1 – 12 (draw diagrams), 25 – 32, 44, 45, 47, 58 – 60