WORKSHEET KEY 1 2 3 4 5 Yes

WORKSHEET KEY 1) 2) 3) 4) 5) Yes No No (6, 6), (– 3, – 3), (0, 3) A’ (– 8, 8), B’ (4, 8), C’ (– 4, – 4) 3/6/2021 3: 10 AM 8) 7/13 9) 4 10) 1/3 11) C 12– 7: Tessellations 1

3/6/2021 3: 10 AM 12– 7: Tessellations 2

MONDAY FUN DAY 3/6/2021 3: 10 AM 12– 7: Tessellations 3

TESSELLATIONS Section 12– 7 Geometry Pre. AP, Revised © 2014 viet. dang@humble. k 12. tx. us 3/6/2021 3: 10 AM 12– 7: Tessellations 4

REVIEW A. Find the sum of the interior angle measures of each polygon. 1. Quadrilateral 2. Octagon 360° 1080° B. Find the interior angle measure of each regular polygon. 1. Square 90° 2. Pentagon 108° 3. Hexagon 120° 4. Octagon 135° 3/6/2021 3: 10 AM 12– 7: Tessellations 5

TESSELLATIONS A. A tessellation, or tiling, A Tessellation is a collection of shapes that fit together to cover a surface without overlapping or leaving gaps. B. Greek word, Tessella which means “four” C. Three regular shapes (all sides and angles) can be made to tessellations 1. Equilateral Triangles: 60° 2. Squares: 90° 3. Hexagons: 120° D. A semiregular tessellation is formed by two or more different regular polygons 3/6/2021 3: 10 AM 12– 7: Tessellations 6

VIDEO http: //www. youtube. com/watch? v=t. JYt. BF 6 gt 4 c 3/6/2021 3: 10 AM 12– 7: Tessellations 7

REAL WORLD EXAMPLES 3/6/2021 3: 10 AM Brick Walls Floor Tiles Checkerboard s Honeycombs Textile Patterns Art 12– 7: Tessellations 8

REGULAR VS SEMIREGULAR TESSELLATION 3/6/2021 3: 10 AM 12– 7: Tessellations 9

REGULAR VS SEMIREGULAR TESSELLATION Regular Tessellations Semi-Regular Tessellations Symmetry in Tessellations 3/6/2021 3: 10 AM 12– 7: Tessellations 10

STEPS A. Rotate the quadrilateral 180° about the midpoint of one side. B. Translate the resulting pair of triangles to make a row C. Translate the row of quadrilaterals to make a tessellation. 3/6/2021 3: 10 AM 12– 7: Tessellations 11

EXAMPLE 1 Copy the given figure and use it to create a tessellation. 3/6/2021 3: 10 AM 12– 7: Tessellations 12

EXAMPLE 2 Copy the given figure and use it to create a tessellation. 3/6/2021 3: 10 AM 12– 7: Tessellations 13

EXAMPLE 3 Classify each tessellation as regular, semiregular, or neither. 3/6/2021 3: 10 AM 12– 7: Tessellations 14

EXAMPLE 4 Classify each tessellation as regular, semiregular, or neither. 3/6/2021 3: 10 AM 12– 7: Tessellations 15

EXAMPLE 4 Classify each tessellation as regular, semiregular, or neither. 3/6/2021 3: 10 AM 12– 7: Tessellations 16

YOUR TURN Classify each tessellation as regular, semiregular, or neither. Then, explain why. 3/6/2021 3: 10 AM 12– 7: Tessellations 17

TYPES OF TESSELLATIONS A. B. C. D. Rotations Translations Reflection Glide Translation 3/6/2021 3: 10 AM 12– 7: Tessellations 18

ROTATIONS A. 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. B. Examples of objects with rotational symmetry include automobile wheels, flowers, and kaleidoscope patterns. 3/6/2021 3: 10 AM 12– 7: Tessellations 19

ROTATIONS 3/6/2021 3: 10 AM 12– 7: Tessellations 20

ROTATIONS 3/6/2021 3: 10 AM 12– 7: Tessellations 21

ROTATIONS 3/6/2021 3: 10 AM 12– 7: Tessellations 22

TRANSLATIONS A. 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. B. A tessellation or pattern with translational symmetry is repeating, like a wallpaper or fabric pattern. 3/6/2021 3: 10 AM 12– 7: Tessellations 23

TRANSLATIONS 3/6/2021 3: 10 AM 12– 7: Tessellations 24

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”. 3/6/2021 3: 10 AM 12– 7: Tessellations 25

REFLECTIONS 3/6/2021 3: 10 AM 12– 7: Tessellations 26

GLIDE REFLECTIONS A. 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. B. A real world example is footsteps! 3/6/2021 3: 10 AM 12– 7: Tessellations 27

GLIDE REFLECTIONS 3/6/2021 3: 10 AM 12– 7: Tessellations 28

ASSIGNMENT Worksheet 3/6/2021 3: 10 AM 12– 7: Tessellations 29