1. Transformations and 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. Properties of Isometries

19. Vocabulary
Ordered Pair Rules – A rule that describes how to transform points on a coordinate plane

20. Transformation - Example

21. Investigation
Get your supplies
Graph paper
Patty Paper

22. Investigation
Fold the graph paper both hot dog and hamburger

23. Investigation
Fold the graph paper both hot dog and hamburger

24. Investigation

25. Investigation

26. Conjectures
The ordered pair rule (x,y) →(-x,y) is a reflection across the y-axis
The ordered pair rule (x,y) →(x,-y) is a reflection across the x-axis
The ordered pair rule (x,y) →(-x,-y) is a rotation about the origin
The ordered pair rule (x,y) →(y,x) is a reflection across the line y = x

27. Homework
7-1 page 372 #1-6, 12-16
7-2 page 381 #1-8, 13-17