Lesson 3

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.

If students are using the applets in the digital versions of the activities, tracing paper may not be needed.