At 10:40 PM 3/25/2010, you wrote:

I'm teaching high school math to homeschoolers and I'm looking for how to make geometry year meaningful.

I'm having a "crisis of confidence" because from my viewpoint, algebra was 10x more useful for future math and science work.

The fact that geometry is considered a place to teach formal reasoning (and not much more) is peculiar to the math standards in this country. Properties of congruent triangles and other trivial stuff can be dispatched with rather quickly (by the end of 6th grade in many countries). I think after that, geometry, more than any other elementary math subject, offers opportunities for creative problem solving. It also teaches transformations and symmetry, invariants (loci of points), creative straightedge and compass constructions, right triangle trigonometry, spacial reasoning, etc. For a creative exploration approach consider http://books.google.com/books?id=tDRJi-qlE18C&printsec=frontcover&dq=%22lines+and+curves%22&source=bl&ots=xPHqn0h_fk&sig=5Ve-5_pEsafkCAcRlDUfYvZFiOU&hl=en&ei=xNCsS6CLKMiVtgfb3KmrDw&sa=X&oi=book_result&ct=result&resnum=1&ved=0CAYQ6AEwAA#v=onepage&q=&f=false. Gary Litvin www.skylit.com