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Opposite angles formed by two intersecting lines are equal, so angle 1 is the same as angle 4. That means angle 1 = angle 5 as well. 

When a line intersects two parallel lines, the corresponding angles are equal. That is, if r and s are parallel, then the angles formed when l intersects r are the same s the angles formed when l intersects s. Angle 1 = Angle 5, Angle 2 = Angle 6, and so forth. Since we know angle 1 = angle 5, so from that you can see that r and s are parallel

Answer:

[tex]r \parallel s[/tex] by the Converse of the Alternate Interiors Angles Theorem.

Step-by-step explanation:

Remember that two lines are parallel if their angle of direction is the same.

So, in this case we know that [tex]m\angle 3 = m\angle 6[/tex], where [tex]\angle 3[/tex] is the direction of [tex]r[/tex] and [tex]\angle 6[/tex] is the direction of [tex]s[/tex].

Therefore, [tex]r \parallel s[/tex] by the Converse of the Alternate Interior Angles Theorem, which states that if two lines are cut by a transversal and the alternate interior angles are congruent, then those lines are parallel.

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