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1. Identify the order and magnitude of rotational symmetry
for a regular triangle.
2. Identify the order and magnitude of rotational symmetry
for a regular quadrilateral.
3. Identify the order and magnitude of rotational symmetry
for a regular hexagon.
4. Identify the order and magnitude of rotational symmetry
for a regular 12-gon.
5. If the point at (–2, 4) is rotated 90° counterclockwise
about the origin, what are the new coordinates?
• Identify regular tessellations.
• Create tessellations with specific attributes.
• tessellation
• regular tessellation
• uniform
• semi-regular tessellation
Regular Polygons
Determine whether a regular 16-gon tessellates the
plane. Explain.
Let 1 represent one interior angle of a regular 16-gon.
m1
Interior Angle Theorem
Substitution
Simplify.
Answer: Since 157.5 is not a
factor of 360,
a 16-gon will not
tessellate the plane.
Determine whether a regular 20-gon tessellates the
plane.
A. yes
B. no
1.
2.
A
B
Semi-Regular Tessellation
Determine whether a semi-regular tessellation can
be created from regular nonagons and squares, all
having sides 1 unit long.
Solve algebraically.
Each interior angle of a regular nonagon measures
or 140°.
Each angle of a square measures 90°. Find whole-number
values for n and s such that
All whole numbers greater than 2 will result in a negative
value for s.
Semi-Regular Tessellation
Substitution
Simplify.
Subtract from
each side.
Divide each side
by 90.
Answer: There are no whole number values
for n and s so that 140n + 90s = 360.
Determine whether a semi-regular tessellation can be
created from regular hexagons and squares, all
having sides 1 unit long.
A. yes
B. no
1.
2.
A
B
Classify Tessellation
STAINED GLASS 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, regular, semi-regular, or
not uniform.
Classify Tessellation
Answer: The pattern is a tessellation because at the
different vertices the sum of the angles is
360°. The tessellation is not uniform because
each vertex does not have the same
arrangement of shapes and angles.
QUILTS Quilt patterns are
often tessellations.
Determine whether the
pattern is a tessellation. If so,
describe it as uniform,
regular, semi-regular, or not
uniform.
A. not a tessellation
B. regular tessellation
C. semi-regular tessellation
D. non-uniform tessellation
1.
2.
3.
4.
A
B
C
D