Question

understanding transversals
use the diagram to complete the
statements.
angles 1 and 5 are
congruent because they
are corresponding angles.
angles 4 and 6 are
congruent because they
are alternate interior
angles.
feedback
lines q and s are parallel. the angles betw
are interior angles.

Explanation:

Step1: Recall angle - pair relationships

When two parallel lines are cut by a transversal, corresponding angles are congruent. Angles 1 and 5 are in the same relative position (corresponding) with respect to the parallel lines \(q\) and \(s\) and the transversal \(r\). So, angles 1 and 5 are congruent because they are corresponding angles.

Step2: Analyze angles 4 and 6

When two parallel lines \(q\) and \(s\) are cut by a transversal (the other non - parallel line in the diagram), alternate interior angles are congruent. Angles 4 and 6 lie between the two parallel lines \(q\) and \(s\) and on opposite sides of the transversal. So, angles 4 and 6 are congruent because they are alternate interior angles.

Answer:

Angles 1 and 5 are congruent because they are corresponding angles. Angles 4 and 6 are congruent because they are alternate interior angles.