Tesselations-This-Classroom-PPt-Final.pptx

Tesselations

1. Tessellations Objective : To understand and construct tessellations using polygons

2. Starter Activity What’s the size of an interior angle of a regular: What’s the size of an exterior angle of a regular: a) square? b) pentagon? c) hexagon? 360 n   a) square? b) pentagon? c) hexagon? 360 4 = 90 o 360 5 = 72 o 360 6 = 60 o 180 – 90 = 90 o 180 – 72 = 108 o 180 – 60 = 100 o

3. Recap Internal angle External angle Size of 1 external angle 360 n = Size of 1 internal angle = 180 – external angle

4. What shapes are used to make up the honeycomb? Can these shapes be arranged so that there are no gaps between them?

5. What does this have to do with tessellations? A regular tessellation is a repeating pattern of a regular polygon, which fits together exactly , leaving NO GAPS. So the bees honeycomb… is a regular tessellation of hexagons

6. Which regular polygons tessellate?

7. Do tessellate  Equilateral Triangles:

8. Which regular polygons tessellate?

9. Squares: Do tessellate 

10. Which regular polygons tessellate?

11. Regular Pentagons: Don’t tessellate

12. Which regular polygons tessellate?

13. Regular Hexagons: Do tessellate 

14. Which regular polygons tessellate?

15. Regular Octagons: Don’t tessellate: This is called a semi-regular tessellation since more than one regular polygon is used.

16. Which regular polygons tessellate?

17. Regular Polygon Size of each exterior angle Size of each interior angle Does this polygon tessellate? Equilateral Triangle Square Regular Pentagon Regular Hexagon Regular Octagon Regular Decagon 180 – 90 = 90 o 180 – 72 = 108 o 180 – 60 = 120 o 180 – 120 = 60 o 180 – 45 = 135 o 180 – 36 = 144 o 360 3 360 4 360 5 360 6 360 8 360 10 = 120 o = 72 o = 45 o = 90 o = 60 o = 36 o Yes No No Yes Yes No 360 60 360 108 360 135 360 90 360 120 360 144 = 6 = 3.33 = 2.67 = 4 = 3 = 2.5

18. There are only 3 regular tessellations. Can you see why? Consider the sum of the interior angles about the indicated point. 60 o 60 o 60 o 60 o 60 o 60 o 6 x 60 o = 360 o 90 o 90 o 90 o 90 o 4 x 90 o = 360 o 120 o 120 o 120 o 3 x 120 o = 360 o 108 o 108 o 108 o 3 x 108 o = 324 o 135 o 135 o 2 x 135 o = 270 o 36 o 90 o

19. Non Regular Tessellations A non-regular tessellation is a repeating pattern of a non-regular polygon, which fits together exactly , leaving NO GAPS. All triangles and all quadrilaterals tessellate.

20. Show that each of these shapes tessellate by drawing at least 8 more around each one. Drawing tessellations c) a) d) b) f) ex. e) g)

21. Drawing tessellations

22. Drawing tessellations

23. Drawing tessellations

24. Drawing tessellations

25. Drawing tessellations

26. Drawing tessellations

27. Drawing Tessellations

28. Drawing tessellations