TESSELLATIO NS Objective To understand construct tessellations using

TESSELLATIO NS Objective: To understand construct tessellations using polygons

Starter Activity 1. 360 n What’s the size of an 2. What’s the size of an interior exterior angle of a regular: a) square? 360 = 90 o 4 180 – 90 = 90 o b) pentagon? 360 = 72 o 5 c) hexagon? 360 = 60 o 6 180 – 72 = 108 o c) hexagon? 180 – 60 = 100 o

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

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

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

Which regular polygons tessellate?

Equilateral Triangles: Do tessellate

Which regular polygons tessellate?

Squares: Do tessellate

Which regular polygons tessellate?

Regular Pentagons: Don’t tessellate

Which regular polygons tessellate?

Regular Hexagons: Do tessellate

Which regular polygons tessellate?

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

Which regular polygons tessellate?

Regular Polygon Equilateral Triangle Size of each exterior angle Size of each interior angle Does this polygon tessellate? 360 = 120 o 3 180 – 120 = 60 o 360 = 6 60 Yes 360 = 90 o 4 180 – 90 = 90 o 360 = 4 90 Yes Regular Pentagon 360 = 72 o 5 180 – 72 = 108 o 360 = 3. 33 108 No Regular Hexagon 360 = 60 o 6 180 – 60 = 120 o 360 = 3 120 Yes Regular Octagon 360 = 45 o 8 180 – 45 = 135 o 360 = 2. 67 135 No Regular Decagon 360 = 36 o 10 180 – 36 = 144 o 360 = 2. 5 144 No Square

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

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

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

Drawing tessellations

Drawing tessellations

Drawing tessellations

Drawing tessellations

Drawing tessellations

Drawing tessellations

Drawing Tessellations

Drawing tessellations