1. Worksheet Key Yes No 8) 7/13 9) 4 10) 1/3
(6, 6), (–6, 6), (–3, –3), (0, 3)
A’ (–8, 8), B’ (4, 8), C’ (–4, –4)
8) 7/13
9) 4
10) 1/3
11) C
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2. 9/18/ :47 AM
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3. Monday Fun Day
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4. Section 12–7 Geometry PreAP, Revised ©2014 viet.dang@humble.k12.tx.us
Tessellations
Section 12–7
Geometry PreAP, Revised ©2014
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5. Review Find the sum of the interior angle measures of each polygon.
Quadrilateral
Octagon
Find the interior angle measure of each regular polygon.
Square
Pentagon
Hexagon
360°
1080°
90°
108°
120°
135°
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6. Tessellations
A tessellation, or tiling, A Tessellation is a collection of shapes that fit together to cover a surface without overlapping or leaving gaps.
Greek word, Tessella which means “four”
Three regular shapes (all sides and angles) can be made to tessellations
Equilateral Triangles: 60°
Squares: 90°
Hexagons: 120°
A semiregular tessellation is formed by two or more different regular polygons
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7. Video http://www.youtube.com/watch?v=tJYtBF6gt4c 9/18/2018 11:47 AM
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8. Real World Examples Brick Walls Floor Tiles Checkerboards Honeycombs
Textile Patterns
Art
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9. Regular vs Semiregular Tessellation
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10. Regular vs Semiregular Tessellation
Regular Tessellations
Semi-Regular Tessellations
Symmetry in Tessellations
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11. Steps Rotate the quadrilateral 180° about the midpoint of one side.
Translate the resulting pair of triangles to make a row
Translate the row of quadrilaterals to make a tessellation.
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12. Example 1 Copy the given figure and use it to create a tessellation.
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13. Example 2 Copy the given figure and use it to create a tessellation. 
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14. Example 3
Classify each tessellation as regular, semiregular, or neither.
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15. Example 4
Classify each tessellation as regular, semiregular, or neither.
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16. Example 4
Classify each tessellation as regular, semiregular, or neither.
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17. Your Turn
Classify each tessellation as regular, semiregular, or neither. Then, explain why.
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18. Types of Tessellations
Rotations
Translations
Reflection
Glide Translation
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19. Rotations
To rotate an object means to turn it around. Every rotation has a center and an angle. A tessellation possesses rotational symmetry if it can be rotated through some angle and remain unchanged.
Examples of objects with rotational symmetry include automobile wheels, flowers, and kaleidoscope patterns.
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20. Rotations
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21. Rotations
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22. Rotations
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23. Translations
To translate an object means to move it without rotating or reflecting it. Every translation has a direction and a distance. A tessellation possesses translational symmetry if it can be translated (moved) by some distance and remain unchanged.
A tessellation or pattern with translational symmetry is repeating, like a wallpaper or fabric pattern.
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24. Translations
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25. Reflections Translations
A. To reflect an object means to produce its mirror image. Every reflection has a mirror line. A tessellation possesses reflection symmetry if it can be mirrored about a line and remain unchanged. A reflection of an “R” is a backwards “R”.
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26. Reflections
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27. Glide Reflections
A glide reflection combines a reflection with a translation along the direction of the mirror line. Glide reflections are the only type of symmetry that involve more than one step. A tessellation possesses glide reflection symmetry if it can be translated by some distance and mirrored about a line and remain unchanged.
A real world example is footsteps!
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28. Glide Reflections
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29. Assignment
Worksheet
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