Course Guide - USAID Teacher Education Project

Unit 3 GeometryWeek 2, Session 3: Tessellations, Summary1. What are the important concepts?a) Some polygons, combination of polygons, or other non-polygonal shapes that arebased on polygons can tile a plane and cover the surface without any gaps or overlaps.Those shapes are said to tessellate if they can be arranged in this manner in thismanner.b) Certain regular (equilateral, equiangular) polygons can tessellate using onlythemselves. These are called regular tessellations. There are only three of theseregular tessellations: those composed of equilateral triangles, those composed ofsquares, and those composed of regular hexagons.Here is a visual explanation of how these regular polygons form a regulartessellation:http://tinyurl.com/Tessel-Visualc) Semi-regular tessellations can be created by combining regular polygons, as in theoctagon/square design below.d) Consider the case of a parallelogram where a "slide" of the shape is enough tocreate a tessellation. However, while all triangles and quadrilaterals can tile a planesome may need to be rotated or "flipped" in order to form a tessellation.See a visual about this at: http://tinyurl.com/Tessel-Tranformations