As Andrew L has mentioned, Hartshorne's book Geometry: Euclid and Beyond is very good. If you really want a comprehensive book (for yourself, not for the children you teach) then Hartshorne is as comprehensive and synthetic as you can get. It also explains the connections with algebra very well.

Less comprehensive, but very insightful about Greek geometry and its history, is Benno Artmann's Euclid -- The Creation of Mathematics (Springer 1999).