Lesson 4 Menu 1.Identify the order and magnitude of rotational symmetry for a regular triangle. 2.Identify the order and magnitude of rotational symmetry.

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Presentation transcript:

Lesson 4 Menu 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?

Lesson 4 MI/Vocab tessellation regular tessellation uniform semi-regular tessellation Identify regular tessellations. Create tessellations with specific attributes.

Lesson 4 Ex1 Regular Polygons Determine whether a regular 16-gon tessellates the plane. Explain. Answer: Since 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 Theorem m1m1

1.A 2.B Lesson 4 CYP1 A.yes B.no Determine whether a regular 20-gon tessellates the plane.

Lesson 4 Ex2 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.

Lesson 4 Ex2 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 side by 90.

1.A 2.B Lesson 4 CYP2 A.yes B.no Determine whether a semi-regular tessellation can be created from regular hexagons and squares, all having sides 1 unit long.

Lesson 4 Ex3 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

Lesson 4 Ex3 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 Lesson 4 CYP3 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.