In a Temple Seminar (Spring 1995), Don Newman gave a beautiful proof of Morley's trisection theorem that is probably in God's book. However, Satan's worshipers might enjoy the present proof.
Note Added Sept. 9, 1997: Gian-Carlo Rota (``Indiscrete Thoughts'', p. 123) uses Morley's theorem as an example of a theorem whose statement is surprising, but neither its statement, nor any of its known proofs, are beautiful. I disagree. The statement is beautiful, and both Ekhad's and Newman's proofs are gorgeous (in different senses).
Note Added Feb. 17, 1998: Kathy Jensen, a student of W. Edwin Clark at University of Southern Florida, found a typo in a previous version. We thank her. See Clark's message.