> Serra: An angle is two rays that share a common endpoint, provided > that the two rays do not lie on the same line.
Why can't the rays lie on the same line? What about 0 degree and 180 degree angles? Not to mention 360 degrees, etc.
As for the general question of defining angle: to a teacher, I would say to present all three definitions to your class, and discuss the merits and shortcomings of each. If you deem this an interesting question.
To a curriculum developer, I would say: you need not define angle in any particular currently fashionable way. Be informal at first, and show examples of angles. Those will have more impact on the students that the definition.
The definition itself should be rotation-based -- angle as "amount of turning". It has the advantage that you don't have to change definitions when you get to trig, it ties in nicely with turtle and transformational geometry, it does no harm to the Euclidean framework, and it has a lot more meaning to children that the ray-based definition.