Question

what is the relationship between ∠1 and ∠2? match each figure with the angle relationship it shows.
(corresponding angles, alternate exterior angles)

Explanation:

Step 1: Recall Angle Relationships

• Corresponding angles: Angles that are in the same position relative to the parallel lines and the transversal. For example, if we have two parallel lines cut by a transversal, a pair of angles that are both above the lines (or both below) and on the same side of the transversal.
• Alternate exterior angles: Angles that are on the outside of the two parallel lines and on alternate sides of the transversal.

Step 2: Analyze Each Figure

• Top - right figure: $\angle 1$ is above the top parallel line, $\angle 2$ is below the bottom parallel line, and they are on the same side of the transversal. So they are corresponding angles. So this figure matches with "corresponding angles".
• Bottom - right figure (labeled with "alternate exterior angles"): $\angle 1$ and $\angle 2$ are on the outer sides of the two parallel lines and on opposite sides of the transversal, so they are alternate exterior angles. So this figure matches with "alternate exterior angles".

Answer:

First Figure (Top - Left):

The relationship between $\angle 1$ and $\angle 2$ in the top - left figure is alternate interior angles (if we consider the transversal and parallel lines). But for the matching:

• The top - left figure (with two parallel lines and a transversal, $\angle 1$ and $\angle 2$) should be matched with "alternate interior angles" (but in the given options, we have "corresponding angles" and "alternate exterior angles" and maybe others). Wait, let's re - examine:
• The top - right figure: $\angle 1$ and $\angle 2$ are corresponding angles. So the top - right figure matches with "corresponding angles".
• The bottom - right figure (labeled with "alternate exterior angles"): If we have a figure where $\angle 1$ and $\angle 2$ are on the outside of the two parallel lines and on alternate sides of the transversal, it is alternate exterior angles.

Matching:

• Top - right figure (with two parallel lines, transversal, $\angle 1$ above the top line, $\angle 2$ below the bottom line on the same side of the transversal) $

ightarrow$ corresponding angles.

• Bottom - right figure $

ightarrow$ alternate exterior angles.

(Assuming the question is to match the figures: Let's assume the top - right figure (second figure in the top row) matches with "corresponding angles" and the bottom - right figure matches with "alternate exterior angles". Also, the top - left figure: if $\angle 1$ and $\angle 2$ are alternate interior angles, but since the given options are "corresponding angles" and "alternate exterior angles", maybe the top - right is corresponding, bottom - right is alternate exterior.)