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10-8 Polygons and Tessellations

10-8 Polygons and Tessellations. Learning Goal: Students will be able to determine which polygons form a tessellation. . A polygon is…. a many-sided figure a shape with three or more sides. Triangle. A triangle has three sides. 1. 3. 2. Square. A square has four sides. 4. 3. 1.

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10-8 Polygons and Tessellations

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  1. 10-8 Polygons and Tessellations Learning Goal: Students will be able to determine which polygons form a tessellation.

  2. A polygon is… a many-sided figure a shape with three or more sides.

  3. Triangle • A triangle has three sides. 1 3 2

  4. Square • A square has four sides. 4 3 1 2

  5. Pentagon • A pentagon has five sides. 1 5 2 4 3

  6. Hexagon and Heptagon • A hexagon has six sides. (Hexagon and six both have an “x”.) • A heptagon has seven sides. heptagon hexagon

  7. Octagon • An octagon has eight sides. Count the sides. If this octagon was red and had the word “Stop” written on it, then you would know where we see a lot of octagons.

  8. Nonagon • An nonagon has nine sides. Count the sides. What does the word “nonagon” sound like?

  9. Decagon • An decagon has tensides. Count the sides. How many years are in a “decade”?

  10. How many degrees are in each polygon? • There is a formula! • (n-2)(180)= • n= the number of sides the polygon has

  11. What is a Tessellation? • A tessellation is a tiling, kind of like the floor, except it goes on forever. • There must be no overlapping or no gaps.

  12. Regular Tessellations • It must tile a floor (flat surface) with no gaps or overlapping. • The tiles must be regular polygons. (Remember that regular means all the sides and angles are congruent.) • Each vertex must look the same. This is a vertex.

  13. Things We Can Tessellate with These Rules. Hexagons 120°+ 120°+120° = 360° Squares Notice that at the vertex the angles add up to 360°. 90°+ 90°+ 90°+ 90° = 360° Triangles The same thing happens here. 60°+ 60°+ 60°+ 60° + 60°+ 60° = 360°

  14. What Won’t Tessellate Pentagons It makes a gap! 108 °+108 °+108 °= 324° Octagons Now there is an overlap. 135 °+135 °+135 °= 405° Guess what! Any regular polygon with more than six sides will overlap. So the only polygons that will work are the triangle, square, and hexagon.

  15. Semi-Regular Tessellations Semi-regular tessellations are almost the same as regular tessellations, except you can use two or more regular polygons. 3, 6, 3, 6 3, 3, 3, 3, 6 Not a tessellation

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