Chapter 9.5

1. Chapter 9.5 Symmetry

2. Symmetry • Objective: Identify and describe symmetry in geometric figures • A figure has symmetry if there’s a transformation of the figure such that the image coincides with the preimage. • Line symmetry is when a figure can be reflected across a line so that the image coincides with the preimage. • Examples: • - yes, one line -no lines of • of symmetry symmetry

3. Rotational Symmetry • If a figure can be rotated about a point by an angle bigger than O ̊ and less than 360 ̊. The image will coincide with the preimage • The angle of rotational symmetry is the smallest angle through which a figure can be rotated to coincide with itself. The amount of times it coincides as it rotates through 360̊ is called the order of the rotational symmetry • Angle of rotational • Symmetry: 90 ̊ • Order: 4

4. Rotational Symmetry • Examples: • No rotational Yes; 90 ̊ • Symmetry Order: 4

5. Plane symmetry and symmetry about an axis • Plane symmetry: • A three-dimensional figure has plane symmetry if a plane can divide the figure into two congruent reflected halves. • Symmetry about an axis: • A three-dimensional figure has symmetry about an axis if there is a line about which the figure can be rotated so that the image coincides with the preimage

6. Examples • 1.) 2.) (equilateral triangular prism) • Symmetry about an axis Plane symmetry and symmetry • about an axis