Question

which two statements belong in a definition of parallel lines?
a. lines that are coplanar
b. lines that do not intersect
c. lines that make right angles
d. lines that have a transversal
e. lines that make vertical angles

Explanation:

To determine the two statements for the definition of parallel lines, we recall the definition: Parallel lines are coplanar lines that do not intersect (in the context of Euclidean geometry).

• Option A: Coplanar lines are part of the definition as parallel lines lie in the same plane.
• Option B: Lines that do not intersect is a key part of the definition of parallel lines.
• Option C: Lines that make right angles define perpendicular lines, not parallel.
• Option D: A transversal is a line that intersects two or more lines, but it is not part of the definition of parallel lines themselves.
• Option E: Vertical angles are formed by intersecting lines, so this is not related to parallel lines.

So the two correct statements are A and B.

Answer:

A. lines that are coplanar, B. lines that do not intersect