An Investigation of Translational Symmetry

Using Geometer's Sketchpad

Let's investigate translational symmetry and how it relates to other types of symmetry. As you investigate, be sure to write down your observations. After you are done, close the sketch without saving your changes!

An image has Translational Symmetry if it can be divided by straight lines into a sequence of identical figures. Translational symmetry results from moving a figure a certain distance in a certain direction also called translating (moving) by a vector (length and direction).

An image has Reflectional Symmetry if there is at least one line which splits the image in half so that one side is the mirror image of the other. Reflectional symmetry is also called line symmetry or mirror symmetry because there is a line in the figure where a mirror could be placed, and the figure would look the same.

An image has Rotational Symmetry if there is a point in the image that the image can be turned around a certain number of degrees and still look the same.

1a) What happens to the green polygon when you move point S?

2a) What happens when the Blue Angle gets bigger or smaller?

3a) What happens when the Red Angle gets bigger or smaller?

4) What happens when the red and blue lines are parallel?

5) How are translation and reflection related?

6) What happens when the red and blue lines intersect?

7) How are reflection and rotation related?