Pantograph
This sketch is inspired by a lesson taught by Keegan Ferris and Becky Simon working with Paul Yu.
See:
http://gvsujenison.weebly.com/
http://beckysimon23.wordpress.com/2014/03/20/teaching-technology-lessons/
http://ferrisksite.wordpress.com/2014/03/28/incorporating-technology-into-math-ed-lessons/
and the pantograph sketch they used from LingguoBu
http://www.geogebratube.org/material/show/id/1515
Like LingguoBu's sketch, this lets you change the proportions in the pantograph. (Click on the Settings checkbox) Does the pantograph always draw similar figures? How can you tell? How do the settings relate to scale factor or magnitude?
More GeoGebra at mathhombre.blogspot.com