Theory:

Let us recall the angles associated with parallel lines, to verify that the drawn \(2\) lines are parallel.
 
Consider \(2\) lines \(m\) and \(n\), which is cut by another line (\(l\)) which makes \(8\) angles intersecting the \(2\) lines.
 
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Vertically opposite angles:
 
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Consider the pair of angles \(\angle 1\), \(\angle 3\); \(\angle 2\), \(\angle 4\); \(\angle 5\), \(\angle 7\); \(\angle 6\), \(\angle 8\). From the above figure, these pair of angles share the same vertex, and they are opposite to each other. These pair of angles are called vertically opposite angles, and these opposite angles are equal.
 
Corresponding angles:
 
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Consider the pair of angles \(\angle 1\), \(\angle 5\); \(\angle 2\), \(\angle 6\); \(\angle 3\), \(\angle 7\) and \(\angle 4\), \(\angle 8\) are corresponding angles. Also, the pair of corresponding angles are equal.
 
Alternate interior angles:
 
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Consider the pair of angles \(\angle 4\), \(\angle 6\) and \(\angle 3\), \(\angle 5\) are alternate interior angles. Also, the pair of alternate interior angles are equal.
 
Alternate exterior angles:
 
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Consider the pair of angles \(\angle 1\), \(\angle 7\) and \(\angle 2\), \(\angle 8\) are alternate exterior angles. Also, these alternate exterior angles are equal.
 
Using any one of these properties, we can prove that the \(2\) lines are parallel.