A parallelogram is a four sided figure that has two pairs of parallel, opposite sides.

Given a parallelogram ABCD,
Since it is a parallelogram,
[tex]\begin{gathered} \bar{AB}=\bar{CD} \\ \bar{AD}=\bar{BC} \end{gathered}[/tex]Also,
[tex]\bar{AB}\parallel\bar{CD}[/tex]Therefore, the line segment parallel to CD passing through A , must fall on AB.