How would I start going about proving these properties?

Prove that the following three properties of a CONNECTED graph $G$ are equivalent:

1. $G$ has no cycles.
2. $G$ is a graph on $N$ vertices with $N-1$ edges.
3. Removing an edge from $G$ disconnects the graph.

I understand that if you remove an edge from a graph that has no cycles, it will disconnect a node.