The puzzle at the end you can do it with only moving two matches to make seven equilateral triangles.
*** Spoiler (select the text to see it... or just look at the image) ***
Make an incomplete Star of David. Take two matches from any triangle and put them on top of another triangle such that you make 3 small equilateral triangles. If you are still counting the large triangle. Then destroy two triangles to make it or put a match on top that is parallel to a side so that it makes another equilateral triangle and repeat: http://imgur.com/VnFuj0l Yeah I realized it probably looks nicer if you just do it on one triangle with three parallel matches instead of two triangles each with two parallel matches.