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:

Step1: Analyze Top - left Figure

In the top - left figure, we have two parallel lines cut by a transversal. ∠1 and ∠2 are in the same relative position with respect to the parallel lines and the transversal. By the definition of corresponding angles, when two parallel lines are cut by a transversal, corresponding angles are equal. So this figure shows corresponding angles.

Step2: Analyze Bottom - right Figure

In the bottom - right figure, ∠1 and ∠2 are formed by two intersecting lines (the transversal and one of the parallel lines). Vertical angles are the non - adjacent angles formed by two intersecting lines. So ∠1 and ∠2 here are vertical angles.

Answer:

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