# Exploring Geometric Transformations in a Dynamic Environment

## Description

These GeoGebra applets with accompanying activities allow exploration of four geometric transformations taught in middle and high school level geometry classes.  The design of the applets provides flexibility of content and grade level with hidden elements that can be revealed to create additional topics for investigating reflections, rotations, translations, and glide-reflections.  Suggested activities and exercises are included but can be altered or omitted to accommodate various levels of mathematical understanding.  The interactive sketches were initially created for use with pre-service teachers in content mathematics education courses at the university level but can also be adapted for middle and high school students.

GeoGebra is an open source exploration/development tool that allows the creation of applets using a Java-based "player" understood by most browsers. If you have difficulty loading the applet, see www.geogebra.org for more information on the system/browser/java requirements for viewing GeoGebra applications.

## Activity 1: Exploring Reflections

This applet and accompanying activities illustrate the reflection of a figure across a line in the plane, including exploration of how the reflection affects measurements such as distance and rectangular coordinates.

Open the pdf activity file and applet in separate windows (or print the pdf file instead) so you can work through the suggested activities.

## Activity 2: Exploring Rotations

This applet and accompanying activities illustrate the rotation of a figure about a point in the plane, including exploration of how the rotation affects rectangular coordinates.

Open the pdf activity file and applet in separate windows (or print the pdf file instead) so you can work through the suggested activities.

## Activity 3: Exploring Translations

This applet and accompanying activities illustrate the translation of a figure by a given vector in the plane, including exploration of how the translation affects rectangular coordinates.

Open the pdf activity file and applet in separate windows (or print the pdf file instead) so you can work through the suggested activities.

## Activity 4: Exploring Glide-Reflections

This applet and accompanying activities illustrate the glide-reflection of a figure (that is, reflection across a line in the plane together with a translation by a vector parallel to the line of reflection) including exploration of how the glide-reflection affects rectangular coordinates.

Open the pdf activity file and applet in separate windows (or print the pdf file instead) so you can work through the suggested activities.

## Activity 5: Exploring Two Reflections with Parallel Lines

This applet and accompanying activities illustrate the effect of the composition of two reflections across parallel lines in the plane.

Open the pdf activity file and applet in separate windows (or print the pdf file instead) so you can work through the suggested activities.

## Activity 6: Exploring Three Reflections with Parallel Lines

This applet and accompanying activities illustrate the effect of the composition of three reflections across parallel lines in the plane.

Open the pdf activity file and applet in separate windows (or print the pdf file instead) so you can work through the suggested activities.

## Activity 7: Exploring Reflections with Intersecting Lines

This applet and accompanying activities illustrate the effect of the composition of two reflections across intersecting lines in the plane.

Open the pdf activity file and applet in separate windows (or print the pdf file instead) so you can work through the suggested activities.

## Activity 8: Exploring Reflections with Concurrent Lines

This applet and accompanying activities illustrate the effect of the composition of three reflections across concurrent lines in the plane.

Open the pdf activity file and applet in separate windows (or print the pdf file instead) so you can work through the suggested activities.