Question

classify ∠1 and ∠2 on the diagram as corresponding, alternate interior, alternate exterior, consecutive (same - side) interior, or consecutive (same - side) exterior angles.

Explanation:

Step1: Recall angle - pair definitions

Corresponding angles are in the same relative position, 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 (same - side) interior angles are between the parallel lines and on the same side of the transversal, and consecutive (same - side) exterior angles are outside the parallel lines and on the same side of the transversal.

Step2: Analyze each case

Case 3

The angles ∠1 and ∠2 are between the parallel lines and on the same side of the transversal. So they are consecutive (same - side) interior angles.

Case 4

The angles ∠1 and ∠2 are in the same relative position with respect to the parallel lines and the transversal. So they are corresponding angles.

Case 5

The angles ∠1 and ∠2 are outside the parallel lines and on opposite sides of the transversal. So they are alternate exterior angles.

Case 6

The angles ∠1 and ∠2 are between the parallel lines and on opposite sides of the transversal. So they are alternate interior angles.

Case 7

The angles ∠1 and ∠2 are between the parallel lines and on the same side of the transversal. So they are consecutive (same - side) interior angles.

Case 8

The angles ∠1 and ∠2 are outside the parallel lines and on the same side of the transversal. So they are consecutive (same - side) exterior angles.

Answer:

1. Consecutive (same - side) interior angles
2. Corresponding angles
3. Alternate exterior angles
4. Alternate interior angles
5. Consecutive (same - side) interior angles
6. Consecutive (same - side) exterior angles