Question

1. choose the correct answer.

which theorem or postulate shows that \\( \angle 1 \cong \angle 8 \\)?
alternate interior angles theorem
corresponding angles postulate
vertical angles theorem
alternate exterior angles theorem

Explanation:

• Alternate Interior Angles Theorem: Applies to angles inside the two parallel lines and on opposite sides of the transversal. ∠1 and ∠8 are not interior angles.
• Corresponding Angles Postulate: Angles in the same relative position. ∠1 and ∠8 are not in corresponding positions.
• Vertical Angles Theorem: Relates angles that are opposite each other at an intersection. ∠1 and ∠8 are not vertical angles.
• Alternate Exterior Angles Theorem: When two parallel lines (\(l\) and \(m\)) are cut by a transversal (\(t\)), alternate exterior angles are congruent. ∠1 and ∠8 are on the outside of the parallel lines \(l\) and \(m\) and on opposite sides of the transversal \(t\).

Answer:

Alternate Exterior Angles Theorem