Question

the figure shows a transversal that intersects two parallel lines. none of the angles are right angles. decide whether each pair of angles is congruent or not congruent. angles: ∠2 and ∠5, congruent or not congruent: ?

Explanation:

Step1: Identify Angle Relationships

When a transversal intersects two parallel lines, corresponding angles, alternate interior angles, and alternate exterior angles are congruent. Vertical angles are also congruent.

Step2: Analyze ∠2 and ∠5

∠2 and ∠5 are same - side interior angles? No, wait. Let's look at their positions. The two parallel lines are cut by a transversal (the horizontal line). ∠2 is on the upper - right of the first intersection, and ∠5 is on the upper - left of the second intersection. ∠2 and ∠5 are same - side interior angles? Wait, no. The sum of same - side interior angles is 180° when lines are parallel, but here we are checking congruence. Corresponding angles would be in the same relative position. ∠2 and, for example, ∠6 would be corresponding (congruent). ∠2 and ∠5: ∠2 is adjacent to ∠1 (supplementary), ∠5 is adjacent to ∠6 (supplementary). Since the two parallel lines are cut by the transversal, ∠2 and ∠5 are same - side interior angles? Wait, no, the horizontal line is the transversal for the two non - horizontal parallel lines. Wait, the two non - horizontal lines are parallel. The horizontal line is the transversal. So ∠2 and ∠5: let's see the positions. ∠2 is between the two parallel lines (interior) and on the right side of the left transversal, ∠5 is between the two parallel lines (interior) and on the left side of the right transversal. So they are same - side interior angles. For parallel lines cut by a transversal, same - side interior angles are supplementary (sum to 180°), not congruent (unless each is 90°, but the problem states no right angles). So ∠2 and ∠5 are not congruent.

Answer:

not congruent