Transcript 9.4 Tessellations

Advanced Geometry
Rigid Transformations
Lesson 4
Tessellations
Symmetry
Figures that are indistinguishable following
a transformation have symmetry.
Tessellation
pattern
no overlapping or empty spaces
On the left is a true tessellation;
on the right is not a tessellation but a pattern.
Tessellations repeat
and have clearly
defined closed shapes.
Patterns repeat but
do not have clearly
defined closed shapes.
Regular Tessellation
one type of REGULAR POLYGON
Equilateral
triangles
Squares
Regular
hexagons
Uniform Tessellation
the same arrangement
of shapes and angles at each vertex
Semi-regular Tessellation
uniform
two or more regular polygons
Example:
Determine whether each polygon tessellates the plane.
If so, describe the tessellation as uniform, not uniform,
regular, or semi-regular.
We must determine if certain polygons
tessellate the plane.
Look at the angle measures at
each vertex to decide.
The angles at every vertex
must have a sum of EXACTLY 360°.
Angles of a Regular Polygon
First find the sum of the
angles of the polygon.
Then divide by the
number of angles.
180(n – 2)
n = # of angles
Sum
n
Example:
Determine whether a regular 16-gon tessellates
the plane. Explain.
Example:
Determine whether each polygon or set of polygons
tessellates the plane. If so, describe the tessellation
as uniform, not uniform, regular, or semi-regular.
Example:
Determine whether a semi-regular tessellation can
be created from each set of figures. Assume that
each figure has side length of 1 unit.
regular pentagon and square
Example:
Determine whether a semi-regular tessellation can
be created from each set of figures. Assume that
each figure has side length of 1 unit.
squares and equilateral triangles
Example:
Stained glass is a very popular design selection for
church and cathedral windows. Determine whether
the pattern is a tessellation. If so, describe it as
uniform, not uniform, regular, or semi-regular.