Book about elementary geometry , triangles, circles ... Currently, I'm studying a little about geometry and I was trying to find out some good book about it on internet, however I didn't find anything that I thought nice to me or what I really expected to which would be nice. What I'm looking for is a book with good proofs, in which show strategies to you reach the solution. and interesting exercises.  For instance :    , ,  ...  Something about mostly elementary geometry, proprieties of triangles, parallels lines, circles, triangle inscribed in a circle, so on.
Book recommendation on plane Euclidean geometry I consider myself relatively good at math, though I don't know it at a high level (yet). One of my problems is that I'm not very comfortable with geometry, unlike algebra, or to restate, I'm much more comfortable with algebra than geometry. I think that's mainly because my geometry education was sparse through the years, lacking in consistency etc. So I'd like to revise (and learn more) all at once, catching the basic axioms, understanding why such is such, etc. Essentially, a moderately rigorous textbook in plain Euclidean geometry (nothing fancy). Please don't say "The Elements" - I have browsed it at the bookstore, it is quite good, but not really what I'm looking for right now.
How to prove a total order has a unique minimal element Let $R$ be a total order on set $S$. Prove that if $S$ has a minimal element, than the minimum element is unique.  I have difficulties with proofs. I know any graph of a total order is a straight line, which clearly has a minimal element. How doI tell when something is mathematically proven?  EDIT: this is how I would prove it  Let $x, y \in S$ such that x and y are minimal. Since S is a total order $x$ and $y$ are comparable and either    case 1: one comes after the other and therefore one isn't the minimal case 2: both are the same and $x=y$  I know this isn't a mathy argument and could use help making it more presentable.