Question

properties of parallel lines quiz
cp geometry a 0 / angles and lines

1. what is line r called and what are ∠1 and ∠2?

image of lines p, q (parallel) and line r (transversal) with ∠1 and ∠2 between them
options:

• line r is the transversal and ∠1 and ∠2 are a linear pair
• line r is the perpendicular bisector and ∠1 and ∠2 are a linear pair
• line r is the perpendicular bisector and ∠1 and ∠2 are consecutive interior angles
• line r is the transversal and ∠1 and ∠2 are consecutive interior angles

Explanation:

1. Recall the definition of a transversal: A transversal is a line that intersects two or more other lines (here, lines \( p \) and \( q \) are parallel, and line \( r \) intersects them). So line \( r \) is a transversal, eliminating options with "perpendicular bisector" (a perpendicular bisector is for segments, not for intersecting parallel lines).
2. Recall the definition of consecutive interior angles: Consecutive interior angles are two angles that lie between the two parallel lines (interior) and on the same side of the transversal. \( \angle 1 \) and \( \angle 2 \) lie between \( p \) and \( q \) (interior) and on the same side of transversal \( r \), so they are consecutive interior angles. A linear pair is two adjacent angles forming a straight line (supplementary), but \( \angle 1 \) and \( \angle 2 \) are not adjacent in the linear pair sense here.

Answer:

D. Line r is the transversal and \( \angle 1 \) and \( \angle 2 \) are consecutive interior angles