1. TransformationsTransformations

2. transformation One to One Mapping Preimage Point  Image Point A change of position or size of a figure. A  A´

3. reflections The mirror image of the original figure * The figures are congruent! * The original image is flipped!

4. Example: Line of Reflection

5. The line of Reflection is also called the line of symmetry.

6. It is also possible to have a reflection image with respect to a point.

7. Point of Symmetry The point must be the midpoint for all segments that pass through it and have endpoints on the figure.

8. Example Does Rhombus MATH have point symmetry? M A T H Yes

9. translation A transformation that moves points the same distance and in the same direction. * The figures are congruent! *Often referred to as a glide!

10. Example:

11. Translations are a composite of Reflections One reflection over another with respect to two parallel lines. l m

12. rotation A transformation that turns a figure about a fixed point. Example: Fixed point

13. Another Example:

14. Rotations are a composite of Reflections One reflection over another with respect to two intersecting lines. l m *Not drawn to scale!

15. Center of rotation The measure of the angle of rotation is twice the measure of the angle formed by the intersecting lines Turn around Point

16. dilation Alters the size of a geometric figure, but does not change its shape.

17. isometry Congruence Transformation –M–Maps every segment to a congruent segment No change in size! –C–Congruent sides and congruent angles

18. State whether each of the following have isometry. Translation Reflection Rotation Dilation Yes No Yes