Draw a line XY intersecting all three lines (transversal) and call the intersections L (AB), M (EF), N (CD).
Angle ALX=angle EMX (corresponding angles on parallel lines)
Angle CNX=angle EMX ( " )
Similarly ALY=EMY and CNY=EMY.
Therefore ALX=CNX and ALY=CNY so the lines AB and CD must be parallel to one another.