12.1 Tessellating Shapes

A tessellation is a pattern made of identical shapes. You can make your own tessellations by fitting copies of a shape together, without gaps or overlaps. 

You say that the shape tessellates, or is a tessellating shape. 

Here are some examples of shapes that tessellate with themselves. 

Here are some examples of shapes that do not tessellate with themselves. There are gaps between the shapes. 

When you make a tessellation you can move the shape by translating, rotating or reflecting it.
For example, here are some of the ways you can tessellate a rectangle. 

Many tesselations are made by repeating a shape and using half-turn rotations of the same shape.

For example, a normal triangle and a half-turn rotation of the same triangle fit together perfectly to make a tessellation like this:

In any tessellations, the sum of the angles at the point where the vertices of the shape meet is 360°.

Look closely the tessellation below:

90° + 90° + 90° + 90° = 360°

Worked Example 12.1

a. Show that the triangle below will tessellate by drawing a tessellation on squared paper.

b. Explain why a regular pentagon will not tessellate. 

Answer: