1. Holt McDougal Geometry Compositions of Transformations Holt Geometry Warm Up Warm Up Lesson Presentation Lesson Presentation Lesson Quiz Lesson Quiz Holt McDougal Geometry 17.2 Symmetry

2. Holt McDougal Geometry Compositions of Transformations Warm Up Determine the coordinates of the image of P(4, –7) under each transformation. 1. a translation 3 units left and 1 unit up 2. a rotation of 90° about the origin (1, –6) (7, 4) 3. a reflection across the y-axis (–4, –7) 17.1

3. Holt McDougal Geometry Compositions of Transformations Diatoms are microscopic algae that are found in aquatic environments. Scientists use a system that was developed in the 1970s to classify diatoms based on their symmetry. A figure has symmetry if there is a transformation of the figure such that the image coincides with the preimage. 17.2

4. Holt McDougal Geometry Compositions of Transformations 17.2

5. Holt McDougal Geometry Compositions of Transformations Example 1: Identifying line of symmetry Yes; four lines of symmetry Tell whether the figure has line symmetry. If so, copy the shape and draw all lines of symmetry. 17.2

6. Holt McDougal Geometry Compositions of Transformations Tell whether each figure has line symmetry. If so, copy the shape and draw all lines of symmetry. Example 2 yes; two lines of symmetry a. b. c. yes; one line of symmetry 17.2

7. Holt McDougal Geometry Compositions of Transformations 17.2

8. Holt McDougal Geometry Compositions of Transformations The angle of rotational symmetry is the smallest angle through which a figure can be rotated to coincide with itself. The number of times the figure coincides with itself as it rotates through 360° is called the order of the rotational symmetry. Angle of rotational symmetry: 90° Order: 4 17.2

9. Holt McDougal Geometry Compositions of Transformations Example 3: Identifying Rotational Symmetry Tell whether each figure has rotational symmetry. If so, give the angle of rotational symmetry and the order of the symmetry. no rotational symmetry yes; 180°; order: 2 yes; 90°; order: 4 A. B. C. 17.2 D. yes; 120°; order: 3

10. Holt McDougal Geometry Compositions of Transformations Example 4: Design Application Describe the symmetry of each icon. Copy each shape and draw any lines of symmetry. If there is rotational symmetry, give the angle and order. No line symmetry; rotational symmetry; angle of rotational symmetry: 180°; order: 2 17.2

11. Holt McDougal Geometry Compositions of Transformations Example 5: Design Application Line symmetry and rotational symmetry; angle of rotational symmetry: 90°; order: 4 Describe the symmetry of each icon. Copy each shape and draw any lines of symmetry. If there is rotational symmetry, give the angle and order. 17.2

12. Holt McDougal Geometry Compositions of Transformations Example 6 Describe the symmetry of each diatom. Copy the shape and draw any lines of symmetry. If there is rotational symmetry, give the angle and order. line symmetry and rotational symmetry; 72°; order: 5 a.b. line symmetry and rotational symmetry; 51.4°; order: 7 17.2