What is preserved under a glide reflection?

Glide reflection changes the orientation: if a polygon is traversed clockwise, its image is traversed counterclockwise, and vice versa. Reflection is isometry: a glide reflection preserves distances. Reflection preserves angles.

What is not always preserved in a reflection?

Reflection does not preserve orientation. Dilation (scaling), rotation and translation (shift) do preserve it.

What properties are preserved under a translation?

Properties preserved under a translation from the pre-image to the image.

• distance (lengths of segments remain the same)
• angle measures (remain the same)
• parallelism (parallel lines remain parallel)
• collinearity (points remain on the same lines)
• orientation (lettering order remains the same)

What is preserved during a translation?

Translation preserves the distance between two points. Translation preserve length. Parallel lines remain parallel.

How are properties preserved under a glide reflection?

Properties preserved (invariant) under a glide reflection: (Since these properties are preserved under both the reflection and the translation, they are preserved under the glide reflection.) 1.   distance is preserved (lengths of segments are the same) 2.   angle measures (remain the same)

What is the difference between trans-flection and glide reflection?

First, a translation is performed on the figure, and then it is reflected over a line. Therefore, Glide reflection is also known as trans-flection. Translation simply means moving, every point of the shape must move the same distance, and in the same direction. Reflection means reflecting an image over a mirror line.

What are glide reflections and congruence in geometry?

Glide Reflections and Congruence. A glide reflection is the composition of a reflection, and a translation in a vector parallel to the line of reflection. This image gets the idea across: (The figure is from Richard Brown’s excellent but dated and out-of-print Transformational Geometry)

How does glide reflection fix a parallel line?

It fixes a system of parallel lines. The isometry group generated by just a glide reflection is an infinite cyclic group. Combining two equal glide reflections gives a pure translation with a translation vector that is twice that of the glide reflection, so the even powers of the glide reflection form a translation group.