Question

question 5 points 2
the construction of parallel lines using a point and a line makes use of the property \_______________\

parallel lines do not intersect.

many transversals can be drawn through a set of parallel lines.

transversals do not intersect.

a transversal makes equal angles of inclination with the paralle lines.

Explanation:

To determine the correct property for constructing parallel lines through a point and a line, we analyze each option:

• "Parallel lines do not intersect" is a basic definition but not the key property used in construction.
• "Many transversals can be drawn through a set of parallel lines" describes a general fact about transversals and parallel lines, not the construction property.
• "Transversals do not intersect" is incorrect as transversals intersect the parallel lines.
• "A transversal makes equal angles of inclination with the parallel lines" (e.g., corresponding angles are equal) is the property used in constructing a parallel line: by creating equal angles with a transversal, we ensure the new line is parallel.

Answer:

D. A transversal makes equal angles of inclination with the parallel lines.