Question

1. choose the correct answer. transversal intersecting two parallel lines which theorem or postulate shows that ∠4 ≅ ∠8? same - side exterior angles theorem alternate interior angles theorem corresponding angles postulate alternate exterior angles theorem

Explanation:

• Same - Side Exterior Angles Theorem: This theorem states that if two parallel lines are cut by a transversal, then the same - side exterior angles are supplementary (their sum is \(180^{\circ}\)), not congruent. So this option is incorrect.
• Alternate Interior Angles Theorem: Alternate interior angles are angles that lie between the two parallel lines and on opposite sides of the transversal. For example, \(\angle3\) and \(\angle5\) are alternate interior angles. \(\angle4\) and \(\angle8\) are not alternate interior angles. So this option is incorrect.
• Corresponding Angles Postulate: Corresponding angles are in the same relative position with respect to the parallel lines and the transversal. \(\angle4\) and \(\angle8\) are in the same relative position (both are in the lower - right position with respect to their respective intersections of the transversal and the parallel lines). When two parallel lines are cut by a transversal, corresponding angles are congruent.
• Alternate Exterior Angles Theorem: Alternate exterior angles lie outside the two parallel lines and on opposite sides of the transversal. \(\angle4\) and \(\angle8\) are not alternate exterior angles. So this option is incorrect.

Answer:

Corresponding Angles Postulate