Folded Rectangle
Jennifer Wilson recently shared some neat activities on what she calls Hopewell triangles. I made this sketch to illustrate these triangles in general.
See:
Hopewell - Right Triangle http://easingthehurrysyndrome.wordpress.com/2013/06/18/hopewell-geometry-right-triangle/
Hopewell - Similarity http://easingthehurrysyndrome.wordpress.com/2013/06/18/hopewell-geometry-similarity/
The problem sheet (pdf)
http://www.map.mathshell.org/materials/download.php?fileid=499