Shape 

Copyright David & Cynthia Thomas, 2009

Symmetry--Challenge: Seeing and Describing Geometric Patterns

Chapter Four focuses on the concept of symmetry and its relationship to the linear transformations of translation (slide), reflection (flip), rotation (turn), and dilation (rescaling).  The following three questions provide a conceptual context in which to consider those properties:

1. What is symmetry and how is it characterized mathematically?

2. What are linear transformations and how are they related to one another and to the concept of congruence?

3. How are symmetry and linear transformations related to plane-coverings such as tilings, friezes, tessellations, and wallpapers?

Challenge: Seeing and Describing Geometric Patterns

Materials needed: Straightedge, protractor, compass    

a.	b.
c.	d.

Figure 4.1: Lines and Points of symmetry

Task: Mark all lines and/or points of symmetry in the objects in Figure 1.  Describe in your own words the relative positions and relationships of the different elements or features of each object.