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?

• tessellation

• regular tessellation

• uniform

• semi-regular tessellation

• Identify regular tessellations.

• Create tessellations with specific attributes.

Regular Polygons

Determine whether a regular 16-gon tessellates the plane. Explain.

Answer: Since 157.5 is not a factor of 360, a 16-gon will not tessellate the plane.

Let 1 represent one interior angle of a regular 16-gon.

Substitution

Simplify.

Interior Angle Theoremm1

1. A

2. B

A. yes

B. no

Determine whether a regular 20-gon tessellates the plane.

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

Answer: There are no whole number values for n and s so that 140n + 90s = 360.

Substitution

Simplify.

Subtract from each side.

Divide each sideby 90.

1. A

2. B

A. yes

B. no

Determine whether a semi-regular tessellation can be

created from regular hexagons and squares, all having sides 1 unit long.

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.

Classify Tessellation

1. A

2. B

3. C

4. D

A. not a tessellation

B. regular tessellation

C. semi-regular tessellation

D. non-uniform tessellation

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.