Answer
$D$
Work Step by Step
Let's take a look at the different options to see which ones are true.
I. If this statement is true, then $l \parallel m$. $\angle 1$ and $\angle 4$ are corresponding angles, so if they are congruent, then the lines are parallel.
II. If this statement is true, then $l \parallel m$. $\angle 2$ and $\angle 5$ are alternate interior angles, so if they are congruent, then the lines are parallel.
III. If this statement is true, then $l \parallel m$. $\angle 3$ and $\angle 4$ are alternate interior angles, so if they are congruent, then the lines are parallel.
IV. If this statement is true, then $l \parallel m$. $\angle 2$ and $\angle 4$ are same-side interior angles, so if they are supplementary, meaning their sum equals $180^{\circ}$, then the lines are parallel.
This means that all the statements are true. Option $D$ reflects this.
