I got a chance to work with a local 8th grade teacher who's looking into Geogebra. He sent me some of the state standards he was interested in exploring, and I made up a couple sketches to play around.
The first is just a demonstration of the area formula for a parallelogram. It seems so unreasonable that all parallelograms with the same base and height have the same area. That connects with one of Geogebra's strengths to me - providing essentially infinite examples so that students can notice.
The next is probably pointless. I was considering how to make a dynamic area measuring sketch. I thought the advantage would be being able to change the figure, and easily check your answer regardless of how you've changed the shape. I used sliders to build the shapes so that the distances would be nice.
Webpage and geogebra file
The third sketch is for similarity - I'll post that later this week with the world's easiest activity.