Symmetry 12-5 I CAN Identify line symmetry, rotational symmetry, and translational symmetry Name the pre-image and image points of a transformation Draw a line of symmetry for a given figure. ●Find the equation of a line of symmetry Holt Geometry

Vocabulary transformation isometry pre-image image

A transformation is a change in the position, size, or shape of a figure or graph. It is sometimes called a mapping. A transformation is a change in the position, size, or shape of a figure or graph. It is sometimes called a mapping. Examples of transformations are: translations, reflections, rotations, and dilations. Examples of transformations are: translations, reflections, rotations, and dilations. A transformation is an isometry if the size and shape of the figure stay the same. Which of the transformations above are an isometry? Translations, reflections, and rotations

Every transformation has a pre-image and an image. Pre-image is the original figure in the transformation (the “before”). Its points are labeled as usual. Image is the shape that results from the transformation (the “after”). The points are labeled with the same letters but with a ' (prime) symbol after each letter.

Example Pre-Image Image A' A B B' C' C

Vocabulary symmetry line symmetry line of symmetry rotational symmetry

A figure has symmetry if there is a transformation of the figure such that the image coincides with the preimage.

Example 1A: Identifying line of symmetry Tell whether the figure has line symmetry. If so, copy the shape and draw all lines of symmetry. yes; eight lines of symmetry

Example 1B: Identifying line of symmetry Tell whether the figure has line symmetry. If so, copy the shape and draw all lines of symmetry. no line symmetry

Example 1C: Identifying line of symmetry Tell whether the figure has line symmetry. If so, copy the shape and draw all lines of symmetry. Yes; four lines of symmetry

a. b. c. Check It Out! Example 1 Tell whether each figure has line symmetry. If so, copy the shape and draw all lines of symmetry. yes; two lines of symmetry a. yes; one line of symmetry b. yes; one line of symmetry c.

Try examples 1 -4 on “Reflections and Symmetry” Handout.

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

Example 2: Identifying Rotational Symmetry Tell whether each figure has rotational symmetry. If so, give the angle of rotational symmetry and the order of the symmetry. A. no rotational symmetry B. yes; 180°; order: 2 C. yes; 90°; order: 4

Check It Out! Example 2 Tell whether each figure has rotational symmetry. If so, give the angle of rotational symmetry and the order of the symmetry. a. b. c. yes; 120°; order: 3 yes; 180°; order: 2 no rotational symmetry

Example 3B: 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. Line symmetry and rotational symmetry; angle of rotational symmetry: 90°; order: 4

Try examples 5 -8 on “Reflections and Symmetry” Handout.

Writing Equations for Lines of Symmetry Remember equations for horizontal lines: y = 2 is horizontal line crossing y-axis at 2 y = –4 is horizontal line crossing y-axis at 4 y=2 y =–4

Writing Equations for Lines of Symmetry Remember equations for vertical lines: x = 2 is vertical line crossing x-axis at 2 x = –4 is vertical line crossing x-axis at –4 x=2 x =–4

Writing Equations for Lines of Symmetry Writing equations in form of y=mx + b m is the slope (rise/run) 2 m =3 2 3 b = 3 Equation of line: y = 3x + 3 2

“Symmetry Worksheet” Practice Problems 1. Equation for line of symmetry_________________

“Symmetry Worksheet” Practice Problems Write the equation of the line of symmetry 2. Equation: ___________________

“Symmetry Worksheet” Practice Problems Write the equation of the line of symmetry 3. Equation: ____________________________

Finish problems for homework