10 8: Polygons and Tesselations Main Idea: classify polygons and determine which polygons can form a tessellation. Vocabulary: polygon A simple closed figure in a plane formed by three or more line segments pentagon A polygon having five sides hexagon A polygon having six sides heptagon A polygon having seven sides octagon A polygon having 8 sides nonagon A polygon having 9 sides decagon A polygon having 10 sides regular polygon A polygon that has all sides congruent and all angle congruent tessellation A repetitive pattern of polygons that fit together with no holes or gaps. 1
These shapes are called polygons. Polygons are flat shapes with sides that are straight line segments. The sides of a polygon do not cross. Polygons are closed figures. triangle rhombus rectangle parallelogram trapezoid square pentagon hexagon octagon 2
POLYGONS Examples Non examples Line segments are called sides. Sides meet only at there end points. Points of intersection are called vertices. Figures with sides that cross each other. Figures that are open Figures that have curved edges. 3
Polygons are made up of sides and vertices. vertices- the place where two sides meet sides- straight lines that make up a figure 4
A shape can be identified by counting the number of sides. 3 sides triangle 4 sides quadrilateral 5 sides pentagon 6 sides hexagon 8 sides octagon 9 sides nonagon 10 sides decagon 5
6
Drag the name of the polygon to it. decagon square pentagon rectangle rhombus heptagon octagon triangle trapezoid hexagon parallelogram nonagon 7
Finding the measure of each angle in each polygon Use the formula (n 2) x 180 Example: Find the measure of the angle in a regular 12 gon (12 2) x 180 12 150 n 8
Polygons Defined Closed, flat figures 3 or more sides Straight sides Corners or angles 9
Let's look at why these shapes are or are not a polygon. A polygon is a closed figure A polygon is a closed figure within a plane that has three or more sides A circle doesn't have sides,angles, or vertex's PULL Click on each shape to reveal answer. 10
PULL Sort the figures into the vortex based on the characteristics of a polygon. 11
Characteristics of a Polygon Three or more sided figure Pull Pull Closed, flat Figure Pull Straight line segments Pull Three or more vertices Pull Three or more angles Pull 12
Tiling with Polygons Some polygons can be used to tile a surface. When you tile, it is important not to overlap tiles or leave gaps between tiles. Tile the large rectangle below by dragging the tiles into place. 13
Tile the following rectangle using the tiles provided. Tile the following rectangle using the tiles provided. Why won't these shapes tile properly? 14
Predict which shapes will tile and which will not. 15
What is a tessellation? A tessellation is a repeated geometric design that covers a plane without gaps or overlaps. Now that you know what tessellation is, use the polygons on the following pages to create tessellated patterns. Move box to reveal answer. 16
Use the polygons to create a tessellated pattern. 17
Use the polygons to create a tessellated pattern. 18
Use the polygons to create a tessellated pattern. HINT: Rotate some of the polygons to create this tessellation. Example 19
Use the polygons to create a tessellated pattern. HINT: Rotate some of the polygons to create this tessellation. Example 20
Assignment p. 549 551, #7 16, 19 21, 34, 35. Review Tomorrow, Test the day after 21
Assignment p. 549 551, #7 16, 19 21, 34, 35. 7. Not a polygon; not all sides congruent 8. Regular octagon 9. Right Triangle, not all sides congruent 10. Not a polygon; curved sides 11. hexagon; not regular 12. Regular decagon 13. 144 14. 140 15. 90 16. 147.3 19. Hexagon and triangle 20. hexagon, square, and triangle 21. Octagons, squares/diamond 34. 60 35. B 22
23