Question

Lines r and s are cut by a transversal as shown which of the following angle pairs , if congruent will help you prove that the lines are parallel

Answer 1

The pair of angles that will prove that the lines are parallel are

angle 2 and angle 6

angle 1 and angle 8

How to find the angles

Angle 2 and angle 6 are corresponding angles

Corresponding angles are pairs of angles formed when a straight line intersects two parallel lines.

In this case, angle 2 and angle 6 are located in corresponding positions at each intersection point. If they are are congruent, then the lines are parallel

angle 1 and angle 8 are alternate exterior angles

Alternate exterior angles are pairs of angles formed when a transversal intersects two parallel lines.

Alternate exterior angles (angle 1 and angle 8) are located on opposite sides of the transversal and on the exterior of the region between the parallel lines. If these angles (angle 1 and angle 8) are congruent, the lines are parallel

Answer 2

III. Angle 2 and Angle 6.

Step-by-step explanation:

Given that the two lines r and s are cut by a transversal such that angles 2 and 6 are congruent.

This congruency implies that angles 2 and 6 are corresponding angles formed by the transversals.

However, this can only occur if the two lines are parallel.

Therefore, the pair of congruent angles that can help prove that the lines are parallel is angle 2 and angle 6.