# Composition of Rigid Motions

## Presentation on theme: "Composition of Rigid Motions"— Presentation transcript:

Composition of Rigid Motions
A sequence of basic rigid motions (translation, rotation, and reflection) “Teaching Geometry According to the Common Core Standards”, H. Wu, 2012

What sequence of basic rigid motions maps the left H exactly onto the right H so that all corresponding angles and segments coincide?

For clarity, we’ll dash the lines of the original H’s
and show in red the image of the left H that will be the subject of our rigid motions.

We draw a straight line segment (a vector) from the lower right corner of the left H to the upper left corner of the right H .

A translation along this vector maps the lower right corner of the red H onto the upper left corner of the right H.

A clockwise rotation of 90 degrees around the red dot maps the right side of the red H to the top side of the right H.

Then a reflection across the top of the right H
maps the red H exactly onto the right H.

To recap: the composition of a translation along a vector, a rotation around a point,

To recap: the composition of a translation along a vector, a rotation around a point, and a reflection across a line is a sequence of basic rigid motions that maps the left H exactly onto the right.