Obj. 33 Symmetry and Tessellations

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Identify and describe symmetry in geometric figures …

Identify and describe symmetry in geometric figures
Use transformations to draw tessellations
Identify regular and semiregular tessellations

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  • 1. Obj. 33 Symmetry & Tessellation The student is able to (I can): • Identify and describe symmetry in geometric figures • Use transformations to draw tessellations • Identify regular and semiregular tessellations
  • 2. symmetry A figure can be transformed such that the image coincides with the preimage. Line symmetry (or reflection symmetry) Rotational symmetry
  • 3. angle of rotational symmetry The smallest angle through which a figure can rotated to coincide with itself. 90º • 60º •
  • 4. Examples Tell whether each figure has line symmetry. If so, how many lines are there? 1. 4 lines of symmetry 2. H 2 lines of symmetry 3. No line symmetry
  • 5. Examples Tell whether each figure has rotational symmetry. If so, give the angle of rotational symmetry. 1. Yes; 120º 2. No rotational symmetry 3. Yes, 45º
  • 6. plane symmetry A plane can divide a three-dimensional figure into two congruent reflected halves. symmetry about an axis There is a line about which a threedimensional figure can be rotated so that the image coincides with the preimage.
  • 7. Examples Tell whether each figure has plane symmetry, symmetry about an axis, or both. 1. Both 2. Plane symmetry
  • 8. tessellation A repeating pattern that completely covers a plane with no gaps or overlaps. Note: The measures of the angles that meet at each vertex must add up to 360º. Because the angle measures of any quadrilateral add to 360º, any quadrilateral can be used to tessellate.
  • 9. regular tessellation A tessellation formed by congruent regular polygons. The only regular polygons that will tesselate are triangles, squares, and hexagons. semiregular tessellation A tessellation formed by two or more different regular polygons with the same number of each polygon occurring in the same order at every vertex.
  • 10. Examples Classify the tessellations as regular, semiregular, or neither. 1. A hexagon meets two squares and a triangle at each vertex. It is semiregular. 2. Only hexagons are used. It is regular. 3. It is neither regular nor semiregular.