Chapter 9.5 and 9.6

1. Chapter 9.5 and 9.6 Symmetry and Dilations

2. Symmetry • A figure has symmetry if there exists a rigid motion- reflection, translation, rotation, or glide reflection- that maps the figure onto itself.

3. Concept

4. Example 1 Identify Line Symmetry A. KALEIDOSCOPES State whether the object appears to have line symmetry. Write yes or no. If so, draw all lines of symmetry, and state their number. Answer: yes; 7 lines of symmetry

5. Example 1 Identify Line Symmetry B. KALEIDOSCOPES State whether the object appears to have line symmetry. Write yes or no. If so, draw all lines of symmetry, and state their number. Answer: no

6. Example 1 Identify Line Symmetry C. KALEIDOSCOPES State whether the object appears to have line symmetry. Write yes or no. If so, draw all lines of symmetry, and state their number. Answer: yes; 5 lines of symmetry

7. Example 1 A. State whether the figure appears to have line symmetry. Write yes or no. If so, state their number. A. yes; 1 line B. yes; 2 lines C. yes; 3 lines D. no

8. Example 1 B. State whether the figure appears to have line symmetry. Write yes or no. If so, state their number. A. yes; 1 line B. yes; 2 lines C. yes; 4 lines D. no

9. Example 1 C. State whether the figure appears to have line symmetry. Write yes or no. If so, state their number. A. yes; 1 line B. yes; 2 lines C. yes; 4 lines D. no

10. Concept

11. Identify Rotational Symmetry A. State whether the figure has rotational symmetry. Write yes or no. If so, locate the center of symmetry and state the order and magnitude of symmetry.

12. Identify Rotational Symmetry B. State whether the figure has rotational symmetry. Write yes or no. If so, locate the center of symmetry and state the order and magnitude of symmetry.

13. Identify Rotational Symmetry C. State whether the figure has rotational symmetry. Write yes or no. If so, locate the center of symmetry and state the order and magnitude of symmetry.

14. Concept

15. Three-Dimensional Symmetry A. State whether the figure has plane symmetry, axis symmetry, both, or neither. Answer: both plane and axis symmetry

16. Example 3 Three-Dimensional Symmetry B. State whether the figure has plane symmetry, axis symmetry, both, or neither. Answer: neither plane nor axis symmetry

17. A. State whether the figure has plane symmetry, axis symmetry, both or neither. A. plane symmetry B. axis symmetry C. both D. neither

18. B. State whether the figure has plane symmetry, axis symmetry, both or neither. A. plane symmetry B. axis symmetry C. both D. neither

19. Dilations • A dilation or scaling is a similarity transformation that enlarges or reduces a figure proportionally with respect to a center point and a scale factor Reduction Enlargement

20. Concept

21. Trapezoid EFGH has vertices E(–8, 4), F(–4, 8), G(8, 4) and H(–4, –8). Graph the image of EFGH after a dilation centered at the origin with a scale factor of Dilations in the Coordinate Plane

22. Dilations • Triangle ABC has the coordinates A (2, 1), B (-1, 3), and C (-2, -2). Graph the image of triangle ABC after a dilation centered at the origin with a scale factor of 2.

23. Scale factor • Find the scale factor if AB = 9 and A’B’ = 3. • Find the scale factor if CD = 5 and C’D’ = 20. • Find the scale factor if XY = 8 and X’Y’ = 12.