1. 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

2. We start with two identical figures.
What sequence of basic rigid motions maps the left H exactly onto the right H so that all corresponding angles and segments coincide?

3. 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.

4. 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 .

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

6. 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.

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

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

9. 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.