Question

what is the relationship between $\angle 1$ and $\angle 2$? match each figure with the angle relationship it shows.

(figure 1: two parallel lines cut by a transversal, $\angle 1$ and $\angle 2$ are...; option: vertical angles)
(figure 2: two parallel lines cut by a transversal, $\angle 1$ and $\angle 2$ are...; option: corresponding angles)

Explanation:

1. For the top - left figure: When a transversal intersects two parallel lines, corresponding angles are in the same relative position. ∠1 and ∠2 are in corresponding positions with respect to the transversal and the parallel lines, so they are corresponding angles.
2. For the bottom - right figure: Vertical angles are formed when two lines intersect, and they are opposite each other. ∠1 and ∠2 are formed by the intersection of two lines (the transversal and one of the parallel lines) and are opposite each other, so they are vertical angles.

Answer:

• Top - left figure (with ∠1 and ∠2): corresponding angles
• Bottom - right figure (with ∠1 and ∠2): vertical angles