Chapter 9.5 Symmetry

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

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

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

Plane symmetry and symmetry about an axis 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

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