1. QuadTessProof

2. Note to Teacher
Challenge the pupils to draw a quadrilateral that won’t tessellate.
They could draw these on the whiteboard.
You can then replicate it using the Geogebra file.
Once they are happy that you can do it every time you can show them a picture proof of the fact that all quadrilaterals tessellate.

3. A Picture Proof that all Quadrilaterals Tessellate
A quadrilateral can be split into two triangles, each containing 180⁰, therefore the sum of the internal angles in a quadrilateral is 360⁰.
Let’s add more tiles identical to the original above, in a systematic way.

4. A Picture Proof that all Quadrilaterals Tessellate

5. A Picture Proof that all Quadrilaterals Tessellate

6. A Picture Proof that all Quadrilaterals Tessellate

7. A Picture Proof that all Quadrilaterals Tessellate

8. A Picture Proof that all Quadrilaterals Tessellate

9. A Picture Proof that all Quadrilaterals Tessellate

10. A Picture Proof that all Quadrilaterals Tessellate

11. A Picture Proof that all Quadrilaterals Tessellate

12. A Picture Proof that all Quadrilaterals Tessellate

13. A Picture Proof that all Quadrilaterals Tessellate
Wherever four tiles meet, each one offers a different angle. These angles are the interior angles of each tile, which we know sum to 360⁰, so there are NO GAPS.