Question

when parallel lines are cut by a transversal, each type of angle pair is either congruent or supplementary. indicate below what the relationship is for each type of angle pair. consecutive exterior angles consecutive interior angles alternate interior angles corresponding angles alternate exterior angles

Explanation:

• Consecutive Exterior Angles: When parallel lines are cut by a transversal, consecutive exterior angles are supplementary. This is because of the properties of parallel lines and the linear - pair and angle - addition postulates.
• Consecutive Interior Angles: Consecutive interior angles are supplementary. If we consider the parallel lines \(l\parallel m\) and a transversal \(t\), using the fact that the sum of angles on the same side of the transversal (either interior or exterior) between two parallel lines is \(180^{\circ}\).
• Alternate Interior Angles: Alternate interior angles are congruent. By the alternate - interior - angles theorem, if two parallel lines are cut by a transversal, then the alternate interior angles are equal in measure.
• Corresponding Angles: Corresponding angles are congruent. According to the corresponding - angles postulate, when two parallel lines are cut by a transversal, corresponding angles have the same measure.
• Alternate Exterior Angles: Alternate exterior angles are congruent. Using the fact that vertical angles are congruent and alternate - interior - angles are congruent (for parallel lines cut by a transversal), we can show that alternate exterior angles are congruent.

Answer:

• Consecutive Exterior Angles: Supplementary
• Consecutive Interior Angles: Supplementary
• Alternate Interior Angles: Congruent
• Corresponding Angles: Congruent
• Alternate Exterior Angles: Congruent