Question

4520va v. geometry sem a
proving lines parallel
which lines are parallel? justify your answer.
lines a and b are parallel because their corresponding angles are congruent.
lines a and b are parallel because their same side exterior angles are congruent.
lines e and f are parallel because their same side exterior angles are supplementary.
lines e and f are parallel because their corresponding angles are congruent.

Explanation:

• For lines \(a\) and \(b\): The angles given (\(110^{\circ}\) and \(110^{\circ}\)) are corresponding angles. By the Corresponding Angles Postulate, if two lines are cut by a transversal and the corresponding angles are congruent, then the lines are parallel.
• For lines \(e\) and \(f\): The sum of the angles (\(110^{\circ}+80^{\circ}=190^{\circ}

eq180^{\circ}\)), so they are not supplementary. Also, the angles are not corresponding angles (one is \(110^{\circ}\), the other is \(80^{\circ}\)).

Answer:

Lines \(a\) and \(b\) are parallel because their corresponding angles are congruent.