# Tessellation Exploration: The Basics

Objective: Find a method to tessellates the plane with any triangle. Introduce regular and semi-regular tessellations.

## Tessellations by Triangles and Quadrilaterals

1. Convince yourself that the parallelogram below will tessellate the plane. Draw your tessellation on a separate piece of paper. It should cover 1/4 of your page.
2. Show that a square tessellates the plane and show that a rectangle tessellates the plane. Your tessellations should cover 1/4 of your page.
3. Draw an acute, an obtuse and a right triangle. Now convince yourself of the fact that two congruent copies of the same triangle fit together to form a parallelogram or a rectangle.
4. Why does this imply that all triangles will tessellate the plane?

## Tessellations of the Plane by Regular Polygons

A regular tessellation is a tessellation made of regular, congruent, convex polygons.

A semi-regular tessellation is a tessellation made of regular polygons of two or more types so that the arrangement of polygons at each vertex is the same.

1. What is the common name for a regular 3-gon?
2. What is the common name for a regular 4-gon?

A tessellation is a regular tessellation if it is constructed from regular convex polygons of one size and one shape. There are exactly three regular polygons that tessellate the plane.