Question

kuta software - infinite geometry
parallel lines and transversals
identify each pair of angles as corresponding, alternate interior, alternate exterior, or consecutive interior.
1)
2)
3)
4)
5)
6)
7)
8)

Explanation:

Step1: Recall angle - pair definitions

Corresponding angles are in the same relative position at each intersection where a transversal crosses parallel lines. Alternate interior angles are between the parallel lines and on opposite sides of the transversal. Alternate exterior angles are outside the parallel lines and on opposite sides of the transversal. Consecutive interior angles are between the parallel lines and on the same side of the transversal.

Step2: Analyze each pair

1. The pair of angles \(x\) and \(y\) are in the same relative position at each intersection, so they are corresponding angles.
2. The pair of angles \(x\) and \(y\) are outside the parallel lines and on opposite sides of the transversal, so they are alternate exterior angles.
3. The pair of angles \(x\) and \(y\) are in the same relative position at each intersection, so they are corresponding angles.
4. The pair of angles \(x\) and \(y\) are outside the parallel lines and on opposite sides of the transversal, so they are alternate exterior angles.
5. The pair of angles \(x\) and \(y\) are between the parallel lines and on opposite sides of the transversal, so they are alternate interior angles.
6. The pair of angles \(x\) and \(y\) are between the parallel lines and on the same side of the transversal, so they are consecutive interior angles.
7. The pair of angles \(x\) and \(y\) are in the same relative position at each intersection, so they are corresponding angles.
8. The pair of angles \(x\) and \(y\) are outside the parallel lines and on opposite sides of the transversal, so they are alternate exterior angles.

Answer:

1. Corresponding
2. Alternate exterior
3. Corresponding
4. Alternate exterior
5. Alternate interior
6. Consecutive interior
7. Corresponding
8. Alternate exterior