Question

the figure shows a transversal that intersects two parallel lines. decide whether each pair of angles is congruent or not congruent. angles: ∠2 and ∠5. options: congruent, not congruent

Explanation:

Step1: Identify Line Types

The two slanted lines are parallel (implied by "a transversal that intersects two [parallel lines]"). The horizontal line is a transversal.

Step2: Analyze Angle Relationship

∠2 and ∠5 are same - side interior angles? Wait, no. Wait, when two parallel lines are cut by a transversal, consecutive interior angles are supplementary, but here ∠2 and ∠5: Wait, actually, ∠2 and ∠5: Let's look at the positions. The two parallel lines (slanted) and the transversal (horizontal). ∠2 and ∠5: Are they alternate interior? No. Wait, maybe the lines: Wait, the two slanted lines are parallel. The horizontal line is a transversal. So ∠2 and ∠5: Let's see, ∠2 and ∠5: if we consider the two parallel lines (slanted) and the transversal (horizontal), then ∠2 and ∠5 are same - side interior angles? Wait, no, maybe I got the lines wrong. Wait, the two slanted lines are parallel, and the horizontal line is a transversal. So ∠2 and ∠5: Let's check the angles. Wait, actually, when two parallel lines are cut by a transversal, corresponding angles are congruent, alternate interior angles are congruent, alternate exterior angles are congruent. But ∠2 and ∠5: Let's see, ∠2 and ∠5: are they same - side interior? Wait, no, maybe the lines are the two horizontal? No, the horizontal is one line. Wait, the two slanted lines are parallel. So the transversal is the horizontal line. So ∠2 and ∠5: Let's look at their positions. ∠2 is between the two slanted lines, above the transversal. ∠5 is also between the two slanted lines, above the transversal? Wait, no, the two slanted lines are parallel, so the distance between them is constant. Wait, maybe ∠2 and ∠5 are same - side interior angles, which are supplementary, not congruent. Wait, but maybe I made a mistake. Wait, no, let's think again. The two slanted lines are parallel. The horizontal line is a transversal. So ∠2 and ∠5: Let's see, ∠2 and ∠5: if we consider the angles formed by the transversal with the two parallel lines. ∠2 and ∠5: are they consecutive interior angles? Yes, because they are on the same side of the transversal (the horizontal line) and between the two parallel lines (the slanted ones). Consecutive interior angles are supplementary, so they are not congruent (unless they are right angles, but there's no indication of that here).

Answer:

not congruent