Geometry in 10th grade back in 1973 was the class that got me interested in mathematics. The teacher told us he was going to prove that the sum of the angles of ALL triangles add up to 180 degrees. I could hardly believe him, there are so many different triangles how could one possibly prove this for all triangles I thought.
Well he did it, and I was very impressed and amazed at the power of the proof. It was all uphill from there.
That said, I am very disapointed in the direction that math education has gone since then. My oldest son took geometry 3 years ago, and it was just learning facts and very little proof. They covered the pathegorean theorem without ever proving it. When I complained to the teacher, she told me not to worry, that they would be covering proofs for two weeks later in the course.
Come again? When I took geometry, with the exception of the postulates, we proved everything. This is what the class was about. As a result we became very skilled and confident logical problem solvers.
Math education today has been very dumbed down compared to the time when I took math in the 1970's and I find this very unfortunate.