Dots and Squares

In the classic game, two players alternate turns, adding a line between two dots.  In a turn, if a player creates a unit square, they claim that square for their score and must then add another line (if two squares are created at once, they still add only a single line.)  When a player places a line and no square is created, the next player takes a turn.  In each puzzle below, it is Player 1's turn.

1. The game has reached the state to the left.  Only one line will guarantee Player 1 the win.  Which one?

2. The game has reached the state to the left.  Player 1 can guarantee a win with what strategy?

3. The game has reached the state to the left.  Player 2 can guarantee a win with what strategy?

Source: Original.