Mathematics Year 9

1
Tessellations
Each of these three diagrams is a fragment of a
tessellation that is made from regular polygons.
c
b
a
2
Tessellations
Sometimes the word tessellation is reserved for
tiling patterns using only one regular polygon,
but here it is used to mean any repeating tiling
pattern.
c
b
a
3
Tessellations
Identify all the polygons and angles. Which
regular polygon fits in each of the outer corners
a ,b and c?
c
b
a
4
Tessellations
The first tessellation has squares and regular
octagons. At each vertex, two octagons meet with
one square, making each angle of the
octagon(360 90) 2 135. The polygon that
fits at corner a is anotheroctagon as the
missingangle is 135.
5
Tessellations
The second tessellation has squares and regular
hexagons. The missing angle at b is360 90
120 150. A regular dodecagon wouldfit in the
corner b.
6
Tessellations
In the third tessellation, an equilateral
triangle meets at a point with two identical
corners of the incomplete polygon. Each of the
polygons interiorangles is (360 60) 2
150,so the polygon which will fitat corner c
is a dodecagon.