We say that a shape tessellates if we can fit together copies of it to cover a flat surface without leaving any gaps and this covering can be extended in all directions.
What about other types of quadrilateral?
Have a go at drawing some quadrilaterals, and finding ways to make them tessellate. You might like to cut a quadrilateral from scrap cardboard and use it to draw around again and again to make a tessellation.
Think about different types of quadrilateral. For example, can you find a way to tessellate any parallelogram? What about a kite? Or a trapezium?
What do you notice about your tessellations?
Do all quadrilaterals tessellate? If your answer is no, give an example of a quadrilateral which doesn’t tessellate. Can you explain why it doesn’t tessellate?
If your answer is yes, can you explain why all quadrilaterals tessellate, and can you give a method which will produce a tessellation of any quadrilateral?
This problem is adapted from the NRICH problem with the same name with permission of the University of Cambridge. All rights reserved.