two lines (AB and CD) are parallel to a third line (EF), then the lines are parallel to each other

Question

Prove that if two lines (AB and CD) are parallel to a third line (EF), then the lines are parallel to each other

Answer 1

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.