Originally Posted by SiaSL
And where does the idea that proofs are limited to geometry come from?!?

Math and multiple choice questions. How... sad.

Yes to everything you wrote.

The better mathematics textbooks in the US have proofs outside of geometry as well. Unfortunately, the mainstream textbooks in this category tend to be older. For example, the high school math textbooks by Richard Brown include proofs outside of geometry (see Algebra 2 here) . Newer programs like AoPS are outstanding math courses and textbooks.