1. Tessellations
A tessellation is made by reflecting, rotating or translating a shape.
A shape will tessellate if it can be used to completely fill a space with no overlapping and no gaps.

2. Tessellating Quadrilaterals
Do all quadrilaterals tessellate?
Yes, quadrilaterals will always tessellate because their interior angles add up to 360°.
So, it is always possible to arrange quadrilaterals together so the angles at a point add to 360°.

3. Tessellation Will a regular pentagon tessellate?
This gap cannot be filled by another regular pentagon.
No, a regular pentagon does not tessellate.
The interior angle of a regular pentagon is 108°.
108° is not a factor of 360°.

4. Tessellation Which three regular polygons will tessellate?
Think about angles that are factors of 360°.
Equilateral triangle. Interior angle = 60°
Square. Interior angle = 90°
Hexagon. Interior angle = 120°