In this third in the sequence of three lessons, students examine tessellations using non-regular polygons. Students show that any triangle can be used to tessellate the plane and similarly for any quadrilateral. Pentagons do not work in general, for example, a regular pentagon cannot be used to tessellate the plane.
Tessellating the plane with a triangle uses the important idea, studied in the sixth grade, that two copies of a triangle can be put together to make a parallelogram. Tessellating the plane with a quadrilateral uses rigid motions of the plane and the fact that the sum of the angles in a quadrilateral is always 360. One example of a plane tessellation with a special pentagon also uses rotations.
- Generalize (orally) that any triangle or quadrilateral can be used to tessellate the plane.
Let’s make tessellations with different polygons.
If students are using the applets in the digital versions of the activities, tracing paper may not be needed.