Chapter 8, Final Exam Review

1. Chapter 8, Final Exam Review Nick DeFeudis

2. Transformations • Getting one set of points from another • When a rule is applied to points in the first set, resulting with a corresponding points in the second set • Definitions: • a transformation is a one-to-one correspondence between two sets of points • Preimage is the set of points before a transformation, and image is the product of the transformation

3. Translations • A translation is a slide, a movement in a single direction of all points • Are also the composite of two subsequent reflections

4. Reflections • A reflection is when the image created is the mirror image of the preimage • The creation of a mirror image is achieved by moving all points across a line of reflection at an equal distance in the image as in the preimage

5. Rotations • Center- point about which the figure is rotated • When a figure is moved about a single point, it is called a rotation

6. Rotations • Distances from the center point in the preimage don’t change in the image • A rotation is also the composite of two successive reflections through intersecting lines

7. Isometries and Congruence • Two figures are congruent if there is an isometry such that one figure is the image of the other • Dilations are not isometries because the shapes are not congruent after the transformation

8. Composite Transformations • An example of a composite transformation is a glide reflection • Glide reflections are the result of three reflections • They can also be considered a translation and a reflection

9. Dilations • A dilationis a transformation where the image and preimage are similar • When the image grows in size, it is an enlargement • When the image shrinks, it is a reduction

10. Rotation Symmetry • Rotational symmetry is when the figure looks exactly the same after a rotation of less than 360 degrees

11. Reflection (Line) Symmetry • A figure has line or reflection symmetry if and only if it coincides with its reflection image through the line

12. Translation Symmetry • A pattern has translation symmetry iff it coincides with a translation image • All points in one shape correspond with points in the other shape

13. Mrs. Liedell’s Quilt Lab • We saw visual representations of transformations in Mrs. Liedell’s quilts. • This unique way of presenting n-fold rotation, lines of reflection, translations and polygons helped to prepare us for the Chapter 8 test.

14. Summary/Key Ideas for Ch. 8 • Transformations (dilation, rotation, translation, reflection) • Kinds of symmetry (line, point, rotational) • Which transformations create similar and congruent figures • Vocab: preimage, image, etc.