**Chapter 2**

**Symmetry and
Transformations**

**
**

This is called **Reflection Symmetry. **The left side of the
image is approximately the same as the right side, but reflected, as
in a mirror, across the line of symmetry. The line of symmetry is
often called a **mirror.**

There are other kinds of symmetry. The stained glass window below,
from Chartres Cathedral in France,** **has **Rotation
Symmetry:**

**Rose Window, Chartres Cathedral, France**

For more information about Chartres Cathedral, click on the link below:

If a tracing of a figure can be rotated less than 180° around
a central point, and matches up with the original, then we say the
figure has **Rotational Symmetry**. In the picture below, you can
see that the Rose Window has 90° rotational symmetry:

**Project**

The project for this chapter is to create a symmetrical geometric
design, such as the examples below. You can create a design with
**Rotation Symmetry**, such as the first one on the **left**
below, or with** Reflection Symmety**, such as the one on the
**right** below. Begin by constructing a simple geometric shape (a
triangle, for example) and then use the Transformations menu to
repeat the shape in a symmetrical pattern. a Sketchpad example is
shown below:

Then you can color your graphic using a computer painting program, or colored pens and pencils. If you do the design using Geometry software (such as the Geometer's SketchPad) it will look better if you Hide the points: first. (To do this, click on the Point tool, choose Edit . . . Select All Points, then Display . . . Hide)

This beautiful geometric image was created by a high school geometry student, using SketchPad and then a painting program:

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