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 9/18/2018 11:47 AM 12–7: Tessellations

9/18/2018 11:47 AM 12–7: Tessellations

Monday Fun Day 9/18/2018 11:47 AM 12–7: Tessellations

Section 12–7 Geometry PreAP, Revised ©2014 viet.dang@humble.k12.tx.us Tessellations Section 12–7 Geometry PreAP, Revised ©2014 viet.dang@humble.k12.tx.us 9/18/2018 11:47 AM 12–7: Tessellations

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° 9/18/2018 11:47 AM 12–7: Tessellations

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 9/18/2018 11:47 AM 12–7: Tessellations

Video http://www.youtube.com/watch?v=tJYtBF6gt4c 9/18/2018 11:47 AM 12–7: Tessellations

Real World Examples Brick Walls Floor Tiles Checkerboards Honeycombs Textile Patterns Art 9/18/2018 11:47 AM 12–7: Tessellations

Regular vs Semiregular Tessellation 9/18/2018 11:47 AM 12–7: Tessellations

Regular vs Semiregular Tessellation Regular Tessellations Semi-Regular Tessellations Symmetry in Tessellations 9/18/2018 11:47 AM 12–7: Tessellations

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. 9/18/2018 11:47 AM 12–7: Tessellations

Example 1 Copy the given figure and use it to create a tessellation. 12–7: Tessellations

Example 2 Copy the given figure and use it to create a tessellation.  12–7: Tessellations

Example 3 Classify each tessellation as regular, semiregular, or neither. 9/18/2018 11:47 AM 12–7: Tessellations

Example 4 Classify each tessellation as regular, semiregular, or neither. 9/18/2018 11:47 AM 12–7: Tessellations

Example 4 Classify each tessellation as regular, semiregular, or neither. 9/18/2018 11:47 AM 12–7: Tessellations

Your Turn Classify each tessellation as regular, semiregular, or neither. Then, explain why. 9/18/2018 11:47 AM 12–7: Tessellations

Types of Tessellations Rotations Translations Reflection Glide Translation 9/18/2018 11:47 AM 12–7: Tessellations

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. 9/18/2018 11:47 AM 12–7: Tessellations

Rotations 9/18/2018 11:47 AM 12–7: Tessellations

Rotations 9/18/2018 11:47 AM 12–7: Tessellations

Rotations 9/18/2018 11:47 AM 12–7: Tessellations

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. 9/18/2018 11:47 AM 12–7: Tessellations

Translations 9/18/2018 11:47 AM 12–7: Tessellations

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”. 9/18/2018 11:47 AM 12–7: Tessellations

Reflections 9/18/2018 11:47 AM 12–7: Tessellations

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! 9/18/2018 11:47 AM 12–7: Tessellations

Glide Reflections 9/18/2018 11:47 AM 12–7: Tessellations

Assignment Worksheet 9/18/2018 11:47 AM 12–7: Tessellations