Transcript Tessellations LESSON 9-7 Additional Examples Identify the repeating figures and a transformation in the tessellation. A repeated combination of an octagon and one adjoining square will.

Tessellations
LESSON 9-7
Additional Examples
Identify the repeating figures and a transformation in the
tessellation.
A repeated combination of an octagon and one adjoining
square will completely cover the plane without gaps or
overlap.
The arrow shows a translation.
Quick Check
HELP
GEOMETRY
Tessellations
LESSON 9-7
Additional Examples
Quick Check
Determine whether a regular 15-gon tessellates a plane.
Explain.
Because the figures in a tessellation do not overlap or leave gaps, the sum
of the measures of the angles around any vertex must be 360°.
Check to see whether the measure of an angle of a regular 15-gon is a
factor of 360.
a=
180 (n – 2)
n
Use the formula for the measure of an angle of a regular
polygon.
a=
180 (15 – 2)
15
Substitute 15 for n.
a = 156
Simplify.
Because 156 is not a factor of 360, a regular 15-gon will not tessellate a plane.
HELP
GEOMETRY
Tessellations
LESSON 9-7
Additional Examples
List the symmetries in the tessellation.
Starting at any vertex, the tessellation can be mapped
onto itself using a 180° rotation, so the tessellation has
point symmetry centered at any vertex.
The tessellation also has translational symmetry,
as can be seen by sliding any triangle onto a copy
of itself along any of the lines.
Quick Check
HELP
GEOMETRY