prooving graph with no cycles and |V | = |E| + 1 is a tree.

My assignment is to prove that G = (V, E) is a tree if and only if |V | = |E| + 1 and G has no cycles.

However, I am having some trouble doing just that.

We defined a tree as a graph which is connected and doesn’t have any cycles so the no cycles part of the proof is given,right? More specifically I can’t figure out how to show that if a graph G = (V, E) has |V | = |E| + 1 and no cycles then it is connected.

Any tips, hints, etc. are welcome.

Thank you