Warm Up

1. Identify Symmetry Warm Up Lesson Presentation Lesson Quiz

2. (8, –3) (–3, 4) ANSWER ANSWER (–8, –3) ANSWER 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 3.Translation 4 units down

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

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

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

6. 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. a.Parallelogram Example 2 Does the figure have rotational symmetry? If so, describe any rotations that map the figure onto itself. SOLUTION

7. b.Regular octagon 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 Example 2 Does the figure have rotational symmetry? If so, describe any rotations that map the figure onto itself. SOLUTION

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

9. 5. Rhombus ANSWER yes; 180° about the center yes; 90° or 180° about the center ANSWER 6. Octagon ANSWER no 7. Right triangle Guided Practice Does the figure have rotational symmetry? If so, describe any rotations that map the figure onto itself.

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

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

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

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

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

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

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