1. Lesson 9-4 Tessellations Tessellation- a pattern that covers a plane by transforming the same figure or set of figures so that there are no overlapping or empty spaces The measure of the angle of the polygon must be a factor of 360 to be able to tessellate. Regular tessellation- formed by one type of polygon Semi-regular tessellation- formed by two or more regular polygons

2. What makes a tessellation Name 3 polygons that make a tessellation Name 3 polygons that do not make a tessellation

3. Determine whether a regular 16-gon tessellates the plane. Explain. Let  1 represent one interior angle of a regular 16-gon. Answer: Since 157.5 is not a factor of 360, a 16-gon will not tessellate the plane. Substitution Simplify. Interior Angle Theorem m1m1

4. Determine whether a regular 20-gon tessellates the plane. Explain. Answer: No; 162 is not a factor of 360.

5. 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 3 will result in a negative value for s.

6. Substitution Simplify. Subtract from each side. Divide each side by 90. Answer: There are no whole number values for n and s so that

7. Determine whether a semi-regular tessellation can be created from regular hexagon and squares, all having sides 1 unit long. Explain. Answer: No; there are no whole number values for h and s such that

8. STAINED GLASS Stained glass is a very popular design selection for church and cathedral windows. It is also fashionable to use stained glass for lampshades, decorative clocks, and residential windows. Determine whether the pattern is a tessellation. If so, describe it as uniform, regular, semi-regular, or not uniform.

9. 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.

10. STAINED GLASS Stained glass is a very popular design selection for church and cathedral windows. It is also fashionable to use stained glass for lampshades, decorative clocks, and residential windows. Determine whether the pattern is a tessellation. If so, describe it as uniform, regular, semi-regular, or not uniform. Answer: tessellation, not uniform