1. 9.6 Warm Up Warm Up Lesson Quiz Lesson Quiz Lesson Presentation Lesson Presentation Identify Symmetry

2. 9.6 Warm-Up Find the coordinates of the image of A(–3, 8) for each transformation. 1. Reflection in the line y = x 2. Rotation of 90º about the origin ANSWER (8, –3) ANSWER (–8, –3) 3. Translation 4 units down ANSWER (–3, 4)

3. 9.6 Example1 SOLUTION How many lines of symmetry does the hexagon have? b.c. a. Two lines of symmetry. b. Six lines of symmetry. c. One line of symmetry. a.

4. 9.6 Guided Practice How many lines of symmetry does the object appear to have? 1. 3. ANSWER 8 5 1 2.

5. 9.6 Guided Practice 4. Draw a hexagon with no lines of symmetry. SAMPLE ANSWER

6. 9.6 Example 2 Does the figure have rotational symmetry? If so, describe any rotations that map the figure onto itself. a. Parallelogram SOLUTION a. The parallelogram has rotational symmetry. The center is the intersection of the diagonals. A 180° rotation about the center maps the parallelogram onto itself.

7. 9.6 Example 2 Does the figure have rotational symmetry? If so, describe any rotations that map the figure onto itself. SOLUTION b. The regular octagon has rotational symmetry.The center is the intersection of the diagonals. Rotations of 45, 90, 135, or 180° about the center all map the octagon onto itself. o o o b. Regular octagon

8. 9.6 Example 2 Does the figure have rotational symmetry? If so, describe any rotations that map the figure onto itself. SOLUTION c. The trapezoid does not have rotational symmetry because no rotation of 180° or less maps the trapezoid onto itself. c. Trapezoid

9. 9.6 Guided Practice Does the figure have rotational symmetry? If so, describe any rotations that map the figure onto itself. 5. Rhombus 6. Octagon 7. Right triangle ANSWERyes; 180° about the center yes; 90° or 180° about the center ANSWER noANSWER

10. 9.6 Example 3 SOLUTION The triangle has line symmetry. Three lines of symmetry can be drawn for the figure.

11. 9.6 For a figure with s lines of symmetry, the smallest rotation that maps the figure onto itself has the measure. So, the equilateral triangle has or 120° rotational symmetry. Example 3 The correct answer is B. 360° s 3

12. 9.6 Guided Practice 8. Describe the lines of symmetry and rotational symmetry of a non-equilateral isosceles triangle. the altitude, no rotational symmetry ANSWER

13. 9.6 Lesson Quiz How many lines of symmetry does each figure have? 1. A Rhombus that is not a square ANSWER 2

14. 9.6 Lesson Quiz How many lines of symmetry does each figure have? 2. Equilateral triangle ANSWER 3

15. 9.6 Lesson Quiz Does the figure have rotational symmetry? If so, describe the rotations that map the figure onto itself. 3. ANSWER Yes ; 72°, 144°

16. 9.6 Lesson Quiz Does the figure have rotational symmetry? If so, describe the rotations that map the figure onto itself. 4. ANSWER no