Section 12-5 Symmetry SPI 32D: determine whether the plane figure has been translated given a diagram and vice versa Objectives: Identify types of Symmetry Symmetry: isometry that maps the figure onto itself Types of symmetry: 1. reflectional or line symmetry 2. rotational symmetry 3. point symmetry Line of Symmetry: Image on one side of the line matches the image on the other side of the line A figure can have more than one line of symmetry

Reflectional or Line Symmetry Line of Symmetry Line of Symmetry

Point Symmetry With point symmetry, a figure looks the same upside down or from two opposite directions Cut a card in half

Judging from appearance, do the letters V and H have rotational symmetry? If so, give an angle of rotation. The letter V does not have rotational symmetry because it must be rotated 360° before it is its own image. The letter H is its own image after one half-turn, so it has rotational symmetry with a 180° angle of rotation. Symmetry

Section 12-6 Tessellations SPI 32D: determine whether the plane figure has been translated given a diagram and vice versa Objectives: Identify transformations and symmetries in Tessellations Tessellation (tiling): A repeated pattern of figures that completely covers a plane, without gaps or overlaps. Can be created with translations, rotations, and reflections

Tesselations Repeated Figure Is the figure a translation or rotation?

Rotational Symmetry Rotation; one fish Translation; horse and rider

Determine if a figure will Tessellate Since figures in a tessellation do not overlap or leave gaps:  the sum of the measures of the angles around the vertex must be 360.  if the angles around the vertex are , then the measure of each angle must be a factor of 360 a = 180(n – 2) n Formula for the measure of an interior angle of a regular polygon a = 180(18 – 2) 18 Substitute a = 160 Simplify Since 160 is not a factor of 360, the 18-gon will not tesselate the plane.

Rotational Symmetry

Graded Activity: 1. Do activity on page 669 in your book 2. Use an index card to make your pattern 3. Use white paper (provided) to draw your tessellation. The whole page must be covered. 4. Color your tessellation.