This is a neat look-see proof that the sum of the exterior angles of any polygon is 360 degrees.
http://www.ies.co.jp/math/java/geo/gaikaku/gaikaku.html

Move the triangle by dragging the red point. What did you find?
http://www.ies.co.jp/math/java/geo/san180/san180.html

You are given a circle of radius 1 unit and two circles of radius a and b which touch each other and also touch the unit circle. Prove that you can always draw a 'flower' with six petals with the unit circle in the middle, and six circles around it having radii
a, b, b/a, 1/a, 1/b and a/b
such that each outer circle touches the unit circle and the two circles on either side of it.
http://nrich.maths.org/public/viewer.php?obj_id=2153

A wonderful interactive implementation of tesselations from the NRich website.
http://nrich.maths.org/public/viewer.php?obj_id=6069

A TI-Nspire activity for investigating opposite angles and angles formed with two lines are cut by a transversal.
http://www.tigeometry.com/activities/cabrijr/239/