Why not some elementary theorems of Euclidan geometry? As I recall, the more general and fundamental theorems were just taken as given in my schooling, but I think many of them can be given accessible and beautiful proofs. Here are some good ones:
1) The Pythagorean theorem. (many lovely proofs)
2) Parallelograms having congruent bases and heights have the same area. (Euclid's proof is pretty.)
3) Use 2 to derive that similar triangles have corresponding sides in common proportion.
4) Two distinct circles have at most 2 points of intersection.
5) Prove the formula for volume of a pyramid without using calculus.