Section 12-5 SymmetrySPI 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 symmetry2. rotational symmetry3. 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 TessellationsSPI 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 ofa 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 book2. Use an index card to make your pattern3. Use white paper (provided) to draw your tessellation. The whole page must be covered.4. Color your tessellation.