# A Teacher's Guide to Investigations of Translational Symmetry Using Geometer's Sketchpad

Students will start by being reminded about the definitions of the types of symmetry.

There is a link to the Sketchpad activity on the Translation page, but not to the questions below.

Students may wish to just explore the Geometry Sketchpad site first before getting a list of questions. There are a few suggestions on the SKETCH, but the list of questions below is more leading for those students who need more guidance.

1a) What happens to the green polygon when you move point S? The green polygon move the same distance and direction as point S is moved.

b) How are the black and green polygons related? The green polygon is a translation of the black polygon by vector RS.

2a) What happens when the Blue Angle gets bigger or smaller? The blue polygon moves.

b)How are the black and the blue polygons related? The black polygon is rotated through the Blue Angle to the blue polygon.

3a) What happens when the Red Angle gets bigger or smaller? The red polygon moves.

b)How are the blue and the red polygons related? The blue polygon is rotated through the Red Angle to the red polygon.

4) What happens when the red and blue lines are parallel? The red polygon (the second reflection) looks like a translation.

5) How are translation and reflection related? A translation is like a double reflection through parallel mirrors.

6) What happens when the red and blue lines intersect? The red polygon (the second reflection) looks like a rotation.

7) How are reflection and rotation related? Reflections through intersection mirrors is like a rotation about the intersection point.