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Identify the repeating figures and a transformation in the tessellation.

A repeated combination of an octagon and one adjoining square will completely cover the plane without gaps or overlap. . The arrow shows a translation. Tessellations. LESSON 9-7. Additional Examples. Identify the repeating figures and a transformation in the tessellation. Quick Check.

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Identify the repeating figures and a transformation in the tessellation.

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  1. A repeated combination of an octagon and one adjoining square will completely cover the plane without gaps or overlap. The arrow shows a translation. Tessellations LESSON 9-7 Additional Examples Identify the repeating figures and a transformation in the tessellation. Quick Check

  2. Use the formula for the measure of an angle of a regular polygon. 180 (15 – 2) 15 180 (n – 2) n a = a = Substitute 15 for n. a = 156 Simplify. Tessellations LESSON 9-7 Additional Examples Quick Check Determine whether a regular 15-gon tessellates a plane. Explain. Because the figures in a tessellation do not overlap or leave gaps, the sum of the measures of the angles around any vertex must be 360°. Check to see whether the measure of an angle of a regular 15-gon is a factor of 360. Because 156 is not a factor of 360, a regular 15-gon will not tessellate a plane.

  3. Starting at any vertex, the tessellation can be mapped onto itself using a 180° rotation, so the tessellation has point symmetry centered at any vertex. The tessellation also has translational symmetry, as can be seen by sliding any triangle onto a copy of itself along any of the lines. Tessellations LESSON 9-7 Additional Examples List the symmetries in the tessellation. Quick Check

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