Chapter 9: Transformations

9.7

Tesselations

Tesselations

• repeating pattern of figures that completely covers a plane without gaps or overlaps

• think: tile, wallpaper, wrapping paper

Example 1• identify a transformation and the repeating

figures in this tessellation

Example 1• identify a transformation and the repeating

figures in this tessellation

Determining a tessellation

• figures in a tessellation do not overlap or leave gaps

• the sum of the measures of the angles around any vertex in a tessellation must be 360°

• if the angles around a vertex are all congruent, then the measure of each angle must be a factor of 360

Example 2

• Determine whether a regular 18-gon tessellates a plane.

Example 2a

• Explain why you can tessellate a plane with an equilateral triangle.

Theorem 9-6

• Every triangle tessellates.

Theorem 9-7

• Every quadrilateral tessellates.

Tessellation Project

• Rules:– each tessellation must be an original drawing– no copy/paste from computer– the tessellation should cover the entire sheet of

paper– tessellations should be colorful, with bold lines

outlining the figure